%-------------------------------------------------------------------------------
% Step 1
%-------------------------------------------------------------------------------

@article{Mu05,
  author =  {M. Mu},
  title =   {{PDE.M}art: A Network-based Problem-solving Environment for {PDE}s},
  journal = {ACM Transactions on Mathematical Software},
  year =    {2005},
  volume =  {31},
  number =  {4},
  pages =   {508--531},
  url =     {https://doi.org/10.1145/1114268.1114272}
}


%-------------------------------------------------------------------------------
% Step 6
%-------------------------------------------------------------------------------

@article{Kel74,
  author =  {R.B. Kellogg},
  title =   {On the {P}oisson equation with intersecting interfaces},
  journal = {Applicable Analysis},
  year  =   {1974},
  volume =  {4},
  number =  {2},
  pages =   {101--129},
  url =     {https://doi.org/10.1080/00036817408839086}
}


%-------------------------------------------------------------------------------
% Step 7
%-------------------------------------------------------------------------------

@article{Li2019,
  author =  {H. Li and X. Zhang},
  title =   {Superconvergence of {C}$^0$-{Q}$^k$ Finite Element Method for Elliptic Equations with Approximated Coefficients},
  journal = {Journal of Scientific Computing},
  year =    {2020},
  month =   dec,
  volume =  {82},
  number =  {1},
  doi =     {10.1007/s10915-019-01102-1},
  url =     {https://doi.org/10.1007/s10915-019-01102-1}
}

@article{KronbichlerWall2018,
  author    = {M. Kronbichler and W.A. Wall},
  title     = {A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers},
  journal   = {SIAM Journal on Scientific Computing},
  year      = {2018},
  volume    = {40},
  number    = {5},
  pages     = {A3423--A3448},
  url       = {https://epubs.siam.org/doi/10.1137/16M110455X},
  doi       = {10.1137/16M110455X}
}


%-------------------------------------------------------------------------------
% Step 10
%-------------------------------------------------------------------------------

@incollection{Cangiani2012,
  author =    {A. Cangiani and J. Chapman and E.H. Georgoulis and M. Jensen},
  title =     {Implementation of the Continuous-Discontinuous {G}alerkin Finite Element Method},
  booktitle = {Numerical Mathematics and Advanced Applications 2011},
  publisher = {Springer Berlin Heidelberg},
  year =      {2012},
  month =     nov,
  pages =     {315--322},
  doi =       {10.1007/978-3-642-33134-3_34},
  url =       {https://doi.org/10.1007/978-3-642-33134-3_34}
}


%-------------------------------------------------------------------------------
% Step 14
%-------------------------------------------------------------------------------

@inproceedings{Ban00w,
  author =    {W. Bangerth},
  title =     {Mesh Adaptivity and Error Control for a Finite Element Approximation of the Elastic Wave Equation},
  booktitle = {Proceedings of the Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation (Waves2000), Santiago de Compostela, Spain, 2000},
  editor =    {Alfredo Berm\'udez and Dolores G\'omez and Christophe Hazard and Patrick Joly and Jean E. Roberts},
  publisher = {SIAM},
  year =      {2000},
  pages =     {725--729}
}

@phdthesis{Ban02,
  author =  {W. Bangerth},
  title =   {Adaptive Finite Element Methods for the Identification of Distributed Parameters in Partial Differential Equations},
  school =  {University of Heidelberg},
  year =    {2002},
  doi =     {10.11588/heidok.00002508},
  url =     {https://doi.org/10.11588/heidok.00002508}
}

@article{BR99b,
  author =  {W. Bangerth and R. Rannacher},
  title =   {Finite element approximation of the acoustic wave equation: Error control and mesh adaptation},
  journal = {East--West Journal of Numerical Mathematics},
  year =    {1999},
  volume =  {7},
  number =  {4},
  pages =   {263--282}
}

@book{BR03,
  author =    {W. Bangerth and R. Rannacher},
  title =     {Adaptive Finite Element Methods for Differential Equations},
  publisher = {Birkh{\"a}user Verlag},
  year =      {2003},
  url =       {https://doi.org/10.1007/978-3-0348-7605-6}
}

@article{BR01a,
  author =  {W. Bangerth and R. Rannacher},
  title =   {Adaptive Finite Element Techniques for the Acoustic Wave Equation},
  journal = {Journal of Computational Acoustics},
  year =    {2001},
  volume =  {9},
  number =  {2},
  pages =   {575--591},
  url =     {https://doi.org/10.1142/S0218396X01000668}
}

@article{BR01,
  author =  {R. Becker and R. Rannacher},
  title =   {An optimal control approach to error estimation and mesh adaptation in finite element methods},
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  year =    {2001},
  volume =  {10},
  pages =   {1--102},
  url =     {https://doi.org/10.1017/S0962492901000010}
}

@phdthesis{Bec95,
  author =  {R. Becker},
  title =   {An Adaptive Finite Element Method for the Incompressible {N}avier--{S}tokes Equations on Time-dependent Domains},
  school =  {Universit{\"a}t Heidelberg},
  year =    {1995},
  url = {https://katalog.ub.uni-heidelberg.de/titel/9608091}
}

@techreport{Bec98,
  author =      {R. Becker},
  title =       {Weighted Error Estimators for the Incompressible {N}avier--{S}tokes Equations},
  institution = {Universit{\"a}t Heidelberg},
  type =        {Preprint 98-20},
  year =        {1998}
}

@article{BR96r,
  author =  {R. Becker and R. Rannacher},
  title =   {A Feed-Back Approach to Error Control in Finite Element Methods: Basic Analysis and Examples},
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  volume =  {4},
  year =    {1996},
  pages =   {237--264}
}

@inproceedings{BR95,
  author =    {R. Becker and R. Rannacher},
  title =     {Weighted A Posteriori Error Control in {FE} Methods},
  booktitle = {ENUMATH 97},
  editor =    {H. G. Bock et al.},
  publisher = {World Scientific Publishing, Singapore},
  year =      {1998},
  pages =     {621--637}
}

@article{FK97,
  author =  {C. F{\"u}hrer and G. Kanschat},
  title =   {A posteriori error control in radiative transfer},
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  year =    {1997},
  volume =  {58},
  number =  {4},
  pages =   {317--334},
  url =     {https://doi.org/10.1007/BF02684345}
}

@phdthesis{Har02,
  author =  {R. Hartmann},
  title =   {Adaptive Finite Element Methods for the Compressible {E}uler Equations},
  school =  {Universit{\"a}t Heidelberg},
  year =    {2002}
}

@article{HH01,
  author =    {R. Hartmann and P. Houston},
  title =     {Adaptive Discontinuous {G}alerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws},
  publisher = {SIAM},
  journal =   {Journal on Scientific Computing},
  year =      {2003},
  volume =    {24},
  number =    {3},
  pages =     {979--1004}
}

@article{HH01b,
  author =  {R. Hartmann and P. Houston},
  title =   {Adaptive Discontinuous {G}alerkin Finite Element Methods for the Compressible {E}uler Equations},
  journal = {Journal of Computational Physics},
  year =    {2002},
  volume =  {183},
  number =  {2},
  pages =   {508--532},
  url =     {https://doi.org/10.1137/S1064827501389084}
}

@phdthesis{Kan96,
  author =  {G. Kanschat},
  title =   {Parallel and Adaptive {G}alerkin Methods for Radiative Transfer Problems},
  school =  {Universit{\"a}t Heidelberg},
  type =    {Dissertation},
  year =    {1996}
}

@article{RS97,
  author =  {R. Rannacher and F.-T. Suttmeier},
  title =   {A feed-back approach to error control in finite element methods: Application to linear elasticity},
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  number =  {5},
  pages =   {434--446},
  url =     {https://doi.org/10.1007/s004660050191}
}

@article{RS98c,
  author =  {R. Rannacher and F.-T. Suttmeier},
  title =   {A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity},
  journal = {Computational Mechanics},
  year =    {1998},
  volume =  {21},
  number =  {2},
  pages =   {123--133},
  url =     {https://doi.org/10.1007/s004660050288}
}

@article{RS99,
  author =  {R. Rannacher and F.-T. Suttmeier},
  title =   {A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    {1999},
  volume =  {176},
  number =  {1},
  pages =   {333--361},
  url =     {https://doi.org/10.1016/S0045-7825(98)00344-2}
}

@phdthesis{Sut96,
  author =  {F.-T. Suttmeier},
  title =   {Adaptive Finite Element Approximation of Problems in Elasto-Plasticity Theory},
  school =  {Universit{\"a}t Heidelberg},
  type =    {Dissertation},
  year =    {1996}
}


%-------------------------------------------------------------------------------
% Step 15
%-------------------------------------------------------------------------------

@book{GNS08,
  author =    {I. Griva and S.G. Nash and A. Sofer},
  title =     {Linear and nonlinear optimization},
  publisher = {SIAM},
  year =      {2008},
  edition =   {2nd},
  url =       {https://doi.org/10.1007/978-1-4939-7055-1}
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@book{NW99,
  author =    {J. Nocedal and S.J. Wright},
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  url =       {https://doi.org/10.1007%2F978-0-387-40065-5}
}

@article{Kelley2022,
  author = { Kelley, C. T. },
  title = { Newton's Method in Mixed Precision },
  journal = { SIAM Review },
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  issue = { 1 },
  pages = { 191--211 },
  doi = {10.1137/20M1342902},
  url = {https://doi.org/10.1137/20M1342902},
}


%-------------------------------------------------------------------------------
% Step 18
%-------------------------------------------------------------------------------

@article{CTZ04,
  author =  {S. Commend and A. Truty and T. Zimmermann},
  title =   {Stabilized finite elements applied to elastoplasticity: I. {M}ixed displacement--pressure formulation},
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  number =  {33},
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  url =     {https://doi.org/10.1016/j.cma.2004.01.007}
}

@article{DL05,
  author =  {H.-Y. Duan and Q. Lin},
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  number =  {9},
  pages =   {1093--1112},
  url =     {https://doi.org/10.1016/j.cma.2004.06.033}
}


%-------------------------------------------------------------------------------
% Step 22
%-------------------------------------------------------------------------------

@article{SW94,
  author =  {D. Silvester and A. Wathen},
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  pages =   {1352--1367},
  url =     {https://doi.org/10.1137/0731070}
}


%-------------------------------------------------------------------------------
% Step 27
%-------------------------------------------------------------------------------

@phdthesis{fehling2020,
  author    = {M. Fehling},
  title     = {Algorithms for massively parallel generic \textit{hp}-adaptive finite element methods},
  publisher = {Forschungszentrum J{\"u}lich GmbH Zentralbibliothek, Verlag},
  school    = {Bergische Universit{\"a}t Wuppertal},
  year      = {2020},
  volume    = {43},
  pages     = {vii, 78 pp},
  url       = {https://juser.fz-juelich.de/record/878206}
}


%-------------------------------------------------------------------------------
% Step 32
%-------------------------------------------------------------------------------

@Article{HDGB17,
  author =       {T. Heister and J. Dannberg and R. Gassm{\"o}ller and W. Bangerth},
  title =        {High Accuracy Mantle Convection Simulation through Modern Numerical Methods. II: Realistic Models and Problems},
  journal =      {Geophysical Journal International},
  year =         2017,
  volume =    210,
  pages =     {833--851}
  }


%-------------------------------------------------------------------------------
% Step 43
%-------------------------------------------------------------------------------

@article{Chueh2010,
  doi = {10.1016/j.compfluid.2010.05.011},
  url = {https://doi.org/10.1016/j.compfluid.2010.05.011},
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@Article{KHB12,
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@article{Chueh2013,
  doi = {10.1137/120866208},
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  journal = {{SIAM} Journal on Scientific Computing}
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@Book{BrezziFortin,
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@Book{Chen2005,
  author =    {Z. Chen},
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@Book{GolubVanLoan,
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@Book{Zhang2005,
  author =    {F. Zhang},
  title =        {The Schur Complement and its Applications},
  publisher =    {Springer},
  year =         {2005}
}


%-------------------------------------------------------------------------------
% Step 47
%-------------------------------------------------------------------------------

@article{Brenner2005,
  author =    {S.C. Brenner and L.-Y. Sung},
  title =     {C$^0$ Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains},
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  url =       {https://doi.org/10.1007/s10915-004-4135-7}
}

@incollection{Brenner2011,
  author =    {S.C. Brenner},
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  doi =       {10.1007/978-3-642-23914-4_2},
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}

@article{Engel2002,
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}

@article{Brenner2010,
  author =    {S.C. Brenner and T. Gudi and L.-Y. Sung},
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@article{Wells2007,
  author =    {G.N. Wells and N.T. Dung},
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  doi =       {10.1016/j.cma.2007.03.008},
  url =       {https://doi.org/10.1016/j.cma.2007.03.008}
}


%-------------------------------------------------------------------------------
% Step 50
%-------------------------------------------------------------------------------

@article{karakashian2003posteriori,
  author =    {O.A. Karakashian and F. Pascal},
  title =     {A posteriori error estimates for a discontinuous {G}alerkin approximation of second-order elliptic problems},
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  volume =    {41},
  number =    {6},
  pages =     {2374--2399},
  url =       {https://doi.org/10.1137/S0036142902405217}
}


%-------------------------------------------------------------------------------
% Step 51
%-------------------------------------------------------------------------------

@article {Ngu2012,
    AUTHOR = {N.C. Nguyen and J. Peraire},
     TITLE = {Hybridizable discontinuous {G}alerkin methods for partial differential equations in continuum mechanics},
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@incollection{F65,
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@article{G65,
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@article {CGL2009,
    AUTHOR = {B. Cockburn and J. Gopalakrishnan and R. Lazarov},
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     PAGES = {1319--1365},
       DOI = {10.1137/070706616},
       URL = {https://doi.org/10.1137/070706616}
}


%-------------------------------------------------------------------------------
% Step 55
%-------------------------------------------------------------------------------

@book{elman2005,
  Author                   = {H.C. Elman and D.J. Silvester and A.J. Wathen},
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@inproceedings{kovasznay1948laminar,
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}


%-------------------------------------------------------------------------------
% Step 57
%-------------------------------------------------------------------------------

@article{Benzi2006,
  author = { M. Benzi and M.A. Olshanskii },
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@article{Yang1998,
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}

@article{Bruneau2006,
  author = { C.-H. Bruneau and M. Saad },
  title = { The 2D lid-driven cavity problem revisited },
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  pages = { 326--348 },
  doi = {10.1016/j.compfluid.2004.12.004},
  url = {https://doi.org/10.1016/j.compfluid.2004.12.004},
}


%-------------------------------------------------------------------------------
% Step 58
%-------------------------------------------------------------------------------

@article{Fraysse2005,
  author = { V. Frayss\'e and L. Giraud and S. Gratton and J. Langou },
  title = { Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers },
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@article{Day2001,
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@article{Axelsson2014,
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@article{Liao2016,
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  url = {https://doi.org/10.1016/j.camwa.2016.09.004},
}


%-------------------------------------------------------------------------------
% Step 59
%-------------------------------------------------------------------------------

@article{Lynch1964,
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  doi = {10.1007/BF01386067},
  journal = {Numerische Mathematik},
  month = {dec},
  pages = {185--199},
  numpages = {15}
}


%-------------------------------------------------------------------------------
% Step 61
%-------------------------------------------------------------------------------

@incollection{Wang2019,
  author =    {Z. Wang and G. Harper and P. O'Leary and J. Liu and S. Tavener},
  title =     {deal.{II} Implementation of a Weak {G}alerkin Finite Element Solver for Darcy Flow},
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  doi =       {10.1007/978-3-030-22747-0_37},
  url =       {https://doi.org/10.1007/978-3-030-22747-0_37}
}


%-------------------------------------------------------------------------------
% Step 63
%-------------------------------------------------------------------------------

@incollection{john2006discontinuity,
  author =    {V. John and P. Knobloch},
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@book{toselli2006domain,
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  year =      {2006},
  volume =    {34},
  url =       {https://doi.org/10.1007/b137868}
}


%-------------------------------------------------------------------------------
% Step 66
%-------------------------------------------------------------------------------

@book{bebernes1989mathematical,
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@phdthesis{castelli2021numerical,
  author    = {G.F. Castelli},
  title     = {Numerical Investigation of {Cahn--Hilliard}-Type Phase-Field Models for Battery Active Particles},
  school    = {Karlsruhe Institute of Technology (KIT)},
  year      = {2021},
  url       = {https://doi.org/10.5445/IR/1000141249}
}

%-------------------------------------------------------------------------------
% Step 67
%-------------------------------------------------------------------------------

@article{KennedyCarpenterLewis2000,
  author =  {C.A. Kennedy and M.H. Carpenter and R.M. Lewis},
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@article{TseliosSimos2007,
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@article{KronbichlerSchoeder2016,
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@article{SchoederKormann2018,
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@article{FehnWallKronbichler2019,
  author =  {N. Fehn and W.A. Wall and M. Kronbichler},
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  year =    {2019},
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  url =     {https://doi.org/10.1002/fld.4683}
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@article{KronbichlerKormann2019,
  author =  {M. Kronbichler and K. Kormann},
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}

@article{Gassner2013,
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  url =     {https://doi.org/10.1137/120890144}
}

%-------------------------------------------------------------------------------
% Step 68
%-------------------------------------------------------------------------------

@article{Blais2013,
  author =    {B. Blais and J.-P. Braeunig and D. Chauveheid and J.-M. Ghidaglia and R. Loub{\`e}re},
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@article{Blais2019,
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@article{Gassmoller2019,
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  number =    {3},
  pages =     {1915--1938},
  url =       {https://doi.org/10.1093/gji/ggz405}
}


%-------------------------------------------------------------------------------
% Step 69
%-------------------------------------------------------------------------------

@article {GuermondPopov2016,
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@article {GuermondPopov2016b,
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@article {GuermondEtAl2018,
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@book {Toro2009,
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  url =       {https:doi.org/10.1007/b79761}
}


%-------------------------------------------------------------------------------
% Step 70
%-------------------------------------------------------------------------------

@inproceedings{Freund1995,
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@article{Riviere1999,
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}


%-------------------------------------------------------------------------------
% Step 71
%-------------------------------------------------------------------------------

@book{Pelteret2019a,
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%-------------------------------------------------------------------------------
% Step 74
%-------------------------------------------------------------------------------

@book{di2011mathematical,
  author =    {D.A. Di Pietro and A. Ern},
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@article{ainsworth2007posteriori,
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  url =       {https://doi.org/10.1137/060665993}
}


%-------------------------------------------------------------------------------
% Step 75
%-------------------------------------------------------------------------------

@book{brenner2008,
  author    = {S. Brenner and R. Scott},
  title     = {The {{Mathematical Theory}} of {{Finite Element Methods}}},
  publisher = {{Springer-Verlag}},
  year      = {2008},
  edition   = {3},
  series    = {Texts in {{Applied Mathematics}}},
  location  = {{New York}},
  url       = {https://www.springer.com/de/book/9780387759333}
}

@article{mitchell2010hpmg,
  author  = {W.F. Mitchell},
  title   = {The \textit{hp}‐multigrid method applied to \textit{hp}‐adaptive refinement of triangular grids},
  journal = {Numerical Linear Algebra with Applications},
  year    = {2010},
  month   = apr,
  volume  = {17},
  number  = {2-3},
  pages   = {211--228},
  url     = {https://doi.org/10.1002/nla.700}
}

@article{mitchell2014hp,
  author  = {W.F. Mitchell and M.A. McClain},
  title   = {A Comparison of \textit{hp}-Adaptive Strategies for Elliptic Partial Differential Equations},
  journal = {ACM Transactions on Mathematical Software},
  year    = {2014},
  volume  = {41},
  number  = {1},
  pages   = {2/1-39},
  doi     = {10.1145/2629459},
  url     = {https://doi.org/10.1145/2629459}
}


%-------------------------------------------------------------------------------
% Step 76
%-------------------------------------------------------------------------------

@article{munch2020hyperdeal,
  doi = {10.1145/3469720},
  url = {https://dl.acm.org/doi/abs/10.1145/3469720},
  year = 2021,
  month = sep,
  publisher = {Association for Computing Machinery ({ACM})},
  volume = 47,
  number = 4,
  pages = {33/1--34},
  author = {P. Munch and K. Kormann and M. Kronbichler},
  title = {hyper.deal: An Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations},
  journal = {{ACM} Transactions on Mathematical Software}
}


%-------------------------------------------------------------------------------
% Step 77
%-------------------------------------------------------------------------------

@article{eiwa96,
  author = {C.E. Stanley and F.W. Homer},
  title = {Choosing the Forcing Terms in an Inexact {N}ewton Method},
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@book{DennisSchnabel96,
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  doi = {10.1137/1.9781611971200},
  URL = {https://epubs.siam.org/doi/abs/10.1137/1.9781611971200}
}


%-------------------------------------------------------------------------------
% Step 78
%-------------------------------------------------------------------------------

@article{black1973pricing,
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  title =   {The Pricing of Options and Corporate Liabilities},
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@article{stoll1969relationship,
  author =    {H.R. Stoll},
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  publisher = {Wiley Online Library},
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  volume =    {24},
  number =    {5},
  pages =     {801--824},
  url =       {https://doi.org/10.1111/j.1540-6261.1969.tb01694.x}
}


%-------------------------------------------------------------------------------
% Step 79
%-------------------------------------------------------------------------------

@book{Bendse2004,
  author =    {M.P. Bends{\o}e and O. Sigmund},
  title =     {Topology Optimization},
  publisher = {Springer Berlin Heidelberg},
  year =      {2004},
  doi =       {10.1007/978-3-662-05086-6},
  url =       {https://doi.org/10.1007/978-3-662-05086-6}
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@book{Nocedal2006,
  author =    {J. Nocedal and S. Wright},
  title =     {Numerical Optimization},
  publisher = {Springer New York},
  year =      {2006},
  doi =       {10.1007/978-0-387-40065-5},
  url =       {https://doi.org/10.1007/978-0-387-40065-5}
}

@article{Waechter2005,
  author =    {A. W\"{a}chter and L.T. Biegler},
  title =     {On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming},
  journal =   {Mathematical Programming},
  publisher = {Springer Science and Business Media {LLC}},
  year =      {2005},
  month =     apr,
  volume =    {106},
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  pages =     {25--57},
  doi =       {10.1007/s10107-004-0559-y},
  url =       {https://doi.org/10.1007/s10107-004-0559-y}
}

@article{Nocedal2009,
  author =    {J. Nocedal and A. W\"{a}chter and R.A. Waltz},
  title =     {Adaptive Barrier Update Strategies for Nonlinear Interior Methods},
  journal =   {SIAM Journal on Optimization},
  publisher = {Society for Industrial {\&} Applied Mathematics (SIAM)},
  year =      {2009},
  month =     jan,
  volume =    {19},
  number =    {4},
  pages =     {1674--1693},
  doi =       {10.1137/060649513},
  url =       {https://doi.org/10.1137/060649513}
}

@article{Benson2002,
  author =    {H.Y. Benson and R.J. Vanderbei and D.F. Shanno},
  title =     {Interior-Point Methods for Nonconvex Nonlinear Programs: Filter Methods and Merit Functions},
  journal =   {Computational Optimization and Applications},
  publisher = {Springer Science and Business Media {LLC}},
  year =      {2002},
  volume =    {23},
  number =    {2},
  pages =     {257--272},
  doi =       {10.1023/a:1020533003783},
  url =       {https://doi.org/10.1023/a:1020533003783}
}

%-------------------------------------------------------------------------------
% Step 81
%-------------------------------------------------------------------------------

@BOOK{Schwartz1972,
  AUTHOR={M. Schwartz},
  TITLE={Principles of Electrodynamics},
  Year={1972},
  PUBLISHER={McGraw-Hill Book Company},
  ADDRESS={New York},
  SERIES={International Series in Pure and Applied Physics},
}

@ARTICLE{berenger1994,
  AUTHOR={J.-P. B\'erenger},
  TITLE={A Perfectly Matched Layer for the Absorption of Electromagnetic Waves},
  JOURNAL={Journal of Computational Physics},
  VOLUME={114},
  PAGES={185-200},
  YEAR={1994},
}

@ARTICLE{Gopalakrishnan2003,
  AUTHOR={J. Gopalakrishnan and J.E. Pasciak},
  TITLE={Overlapping Schwarz preconditioners for indefinite time harmonic {M}axwell equations},
  JOURNAL={Mathematics of Computation},
  VOLUME={72},
  PAGES={1-15},
  YEAR={2003}
}

@BOOK{Monk2003,
  AUTHOR={P. Monk},
  TITLE={Finite Element Methods for {Maxwell's} Equations},
  YEAR={2003},
  PUBLISHER={Oxford University Press},
  SERIES={Numerical Mathematics and Scientific Computation},
}

@ARTICLE{Geim2004,
  AUTHOR={K.S. Novoselov and A.K. Geim and S.V. Morozov and D. Jiang and Y. Zhang and S.V. Dubonos and I.V. Grigorieva and A.A. Firsov},
  TITLE={Electric Field Effect in Atomically Thin Carbon Films},
  JOURNAL={Science},
  VOLUME={306},
  PAGES={666},
  YEAR={2004}
}

@ARTICLE{Maier2017,
  author = {M. Maier and D. Margetis and M. Luskin},
  journal = {Journal of Computational Physics},
  pages = {126--145},
  title = {Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation},
  volume = {339},
  year = {2017}
}

@ARTICLE{Ying2012,
  TITLE={A sweeping preconditioner for time-harmonic {M}axwell's equations},
  AUTHOR={P. Tsuji and B. Engquist and L. Ying},
  YEAR={2012},
  JOURNAL={Journal of Computational Physics},
  VOLUME={231},
  PAGES={3770-3783},
}


%-------------------------------------------------------------------------------
% Step 82
%-------------------------------------------------------------------------------

@article{Pryer2014,
  author = {T. Pryer},
  title = {Discontinuous {G}alerkin methods for the p-biharmonic equation from a discrete variational perspective},
  journal = {Electronic Transactions of Numerical Analysis},
  volume = {41},
  pages = {328--349},
  year = {2014}
}

@article{Bonito2021,
  author = {A. Bonito and R.H. Nochetto and D. Ntogkas},
  title = {{DG} Approach to Large Bending Plate Deformations with Isometry Constraint},
  journal = {Mathematical Models and Methods in Applied Sciences},
  volume = {31},
  number = {1},
  pages = {133--175},
  year = {2021}
}

@book{DiPietro2011,
  author = {D.A. Di Pietro and A. Ern},
  title = {Mathematical Aspects of Discontinuous {G}alerkin Methods},
  series = {Math{\'e}matiques et Applications},
  publisher={Springer Berlin Heidelberg},
  year={2011},
}

@article{BGNY2020,
  doi = {10.1016/j.jcp.2021.110719},
  url = {https://www.sciencedirect.com/science/article/pii/S0021999121006148},
  year = 2022,
  month = jan,
  publisher = {Elsevier {BV}},
  volume = 448,
  pages = {110719/1--27},
  author = {A. Bonito and D. Guignard and R.H. Nochetto and S. Yang},
  title = {{LDG} approximation of large deformations of prestrained plates},
  journal = {Journal of Computational Physics}
}

@article{BGNY2021,
  doi = {10.1093/imanum/drab103},
  url = {https://academic.oup.com/imajna/article/43/2/627/6517084},
  year = 2022,
  month = mar,
  publisher = {Oxford University Press ({OUP})},
  volume = 43,
  number = 2,
  pages = {627--662},
  author = {A. Bonito and D. Guignard and R.H. Nochetto and S. Yang},
  title = {Numerical analysis of the {LDG} method for large deformations of prestrained plates},
  journal = {{IMA} Journal of Numerical Analysis}
}


% ------------------------------------
% Step 83
% ------------------------------------


@article{Young1974,
  doi = {10.1145/361147.361115},
  url = {https://doi.org/10.1145/361147.361115},
  year = {1974},
  month = sep,
  publisher = {Association for Computing Machinery ({ACM})},
  volume = {17},
  number = {9},
  pages = {530--531},
  author = {John W. Young},
  title = {A first order approximation to the optimum checkpoint interval},
  journal = {Communications of the {ACM}}
}


@article{Daly2006,
  doi = {10.1016/j.future.2004.11.016},
  url = {https://doi.org/10.1016/j.future.2004.11.016},
  year = {2006},
  month = feb,
  publisher = {Elsevier {BV}},
  volume = {22},
  number = {3},
  pages = {303--312},
  author = {J.T. Daly},
  title = {A higher order estimate of the optimum checkpoint interval for restart dumps},
  journal = {Future Generation Computer Systems}
}

%-------------------------------------------------------------------------------
% Step 85
%-------------------------------------------------------------------------------

@article{saye_2015,
  title = {High-{Order} {Quadrature} {Methods} for {Implicitly} {Defined} {Surfaces} and {Volumes} in {Hyperrectangles}},
  volume = {37},
  issn = {1064-8275, 1095-7197},
  url = {https://epubs.siam.org/doi/10.1137/140966290},
  doi = {10.1137/140966290},
  language = {en},
  number = {2},
  urldate = {2016-01-27},
  journal = {SIAM Journal on Scientific Computing},
  author = {R.I. Saye},
  month = jan,
  year = {2015},
  pages = {A993--A1019}
}

@article{burman_hansbo_2012,
  title = {Fictitious domain finite element methods using cut elements: {II}. {A} stabilized {Nitsche} method},
  volume = {62},
  issn = {01689274},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0168927411000298},
  doi = {10.1016/j.apnum.2011.01.008},
  language = {en},
  number = {4},
  urldate = {2015-12-17},
  journal = {Applied Numerical Mathematics},
  author = {E. Burman and P. Hansbo},
  month = apr,
  year = {2012},
  pages = {328--341}
}

@article{cutfem_2015,
  title = {{CutFEM}: {Discretizing} geometry and partial differential equations},
  volume = {104},
  issn = {00295981},
  url = {https://doi.wiley.com/10.1002/nme.4823},
  doi = {10.1002/nme.4823},
  language = {en},
  number = {7},
  urldate = {2016-01-27},
  journal = {International Journal for Numerical Methods in Engineering},
  author = {E. Burman and S. Claus and P. Hansbo and M.G. Larson and A. Massing},
  month = nov,
  year = {2015},
  pages = {472--501}
}

%-------------------------------------------------------------------------------
% Step 90
%-------------------------------------------------------------------------------
@InProceedings{traceFEM_review_2017,
  author="Olshanskii, Maxim A.
    and Reusken, Arnold",
  editor="Bordas, St{\'e}phane P. A. and Burman, Erik and Larson, Mats G. and Olshanskii, Maxim A.",
  title="Trace Finite Element Methods for PDEs on Surfaces",
  booktitle="Geometrically Unfitted Finite Element Methods and Applications",
  year="2017",
  publisher="Springer International Publishing",
  pages="211--258",
  isbn="978-3-319-71431-8"
}

%-------------------------------------------------------------------------------
% Step 87
%-------------------------------------------------------------------------------

@article{henri2022geometrical,
  title={Geometrical level set reinitialization using closest point method and kink detection for thin filaments, topology changes and two-phase flows},
  author={Henri, F{\'e}lix and Coquerelle, Mathieu and Lubin, Pierre},
  journal={Journal of Computational Physics},
  volume={448},
  pages={110704},
  year={2022},
  publisher={Elsevier}
}

@article{coquerelle2016fourth,
	title={A fourth-order accurate curvature computation in a level set framework for two-phase flows subjected to surface tension forces},
	author={Coquerelle, Mathieu and Glockner, St{\'e}phane},
	journal={Journal of Computational Physics},
	volume={305},
	pages={838--876},
	year={2016},
	publisher={Elsevier}
}

@article{brackbill1992continuum,
  title={A continuum method for modeling surface tension},
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  journal={Journal of computational physics},
  volume={100},
  number={2},
  pages={335--354},
  year={1992},
  publisher={Elsevier}
}

@article{olsson2005conservative,
  title={A conservative level set method for two phase flow},
  author={Olsson, Elin and Kreiss, Gunilla},
  journal={Journal of computational physics},
  volume={210},
  number={1},
  pages={225--246},
  year={2005},
  publisher={Elsevier}
}

@article{kronbichler2018fast,
  title={A fast massively parallel two-phase flow solver for microfluidic chip simulation},
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  journal={The International Journal of High Performance Computing Applications},
  volume={32},
  number={2},
  pages={266--287},
  year={2018},
  publisher={SAGE Publications Sage UK: London, England}
}

@article{peskin1977numerical,
  title={Numerical analysis of blood flow in the heart},
  author={Peskin, Charles S},
  journal={Journal of computational physics},
  volume={25},
  number={3},
  pages={220--252},
  year={1977},
  publisher={Elsevier}
}

@article{unverdi1992front,
  title={A front-tracking method for viscous, incompressible, multi-fluid flows},
  author={Unverdi, Salih Ozen and Tryggvason, Gr{\'e}tar},
  journal={Journal of computational physics},
  volume={100},
  number={1},
  pages={25--37},
  year={1992},
  publisher={Elsevier}
}

@article{bungartz2016precice,
  title={{preCICE} -- a fully parallel library for multi-physics surface coupling},
  author={Bungartz, Hans-Joachim and Lindner, Florian and Gatzhammer, Bernhard and Mehl, Miriam and Scheufele, Klaudius and Shukaev, Alexander and Uekermann, Benjamin},
  journal={Computers \& Fluids},
  volume={141},
  pages={250--258},
  year={2016},
  publisher={Elsevier}
}

@article{chourdakis2021precice,
  title={{preCICE} v2: A sustainable and user-friendly coupling library},
  author={Chourdakis, Gerasimos and Davis, Kyle and Rodenberg, Benjamin and Schulte, Miriam and Simonis, Fr{\'e}d{\'e}ric and Uekermann, Benjamin and Abrams, Georg and Bungartz, Hans-Joachim and Yau, Lucia Cheung and Desai, Ishaan and others},
  journal={arXiv preprint arXiv:2109.14470},
  year={2021}
}

@article{lebrun2020arborx,
  title={ArborX: A performance portable geometric search library},
  author={Lebrun-Grandi{\'e}, Damien and Prokopenko, Andrey and Turcksin, Bruno and Slattery, Stuart R},
  journal={ACM Transactions on Mathematical Software (TOMS)},
  volume={47},
  number={1},
  pages={1--15},
  year={2020},
  publisher={ACM New York, NY, USA}
}

@article{heinz2022high,
  title={High-Order Non-Conforming Discontinuous {G}alerkin Methods for the Acoustic Conservation Equations},
  author={Heinz, Johannes and Munch, Peter and Kaltenbacher, Manfred},
  journal={International Journal for Numerical Methods in Engineering},
  year={2022},
  volume={124},
  number={9},
  pages={2034-2049},
  publisher={Wiley Online Library}
}



%%% sparse communication pattern

@article{hoefler2010scalable,
  title={Scalable communication protocols for dynamic sparse data exchange},
  author={Hoefler, Torsten and Siebert, Christian and Lumsdaine, Andrew},
  journal={ACM Sigplan Notices},
  volume={45},
  number={5},
  pages={159--168},
  year={2010},
  publisher={ACM New York, NY, USA}
}

@article{burman2015cutfem,
  title={CutFEM: discretizing geometry and partial differential equations},
  author={Burman, Erik and Claus, Susanne and Hansbo, Peter and Larson, Mats G and Massing, Andr{\'e}},
  journal={International Journal for Numerical Methods in Engineering},
  volume={104},
  number={7},
  pages={472--501},
  year={2015},
  publisher={Wiley Online Library}
}


%-------------------------------------------------------------------------------
% Step 89
%-------------------------------------------------------------------------------

@article{hochbruck2014efficient,
  author    = {Marlis Hochbruck and Tomislav Pa{\v{z}}ur and Andreas Schulz and Ekkachai Thawinan and Christian Wieners},
  journal   = {{ZAMM} - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik},
  title     = {Efficient time integration for discontinuous {G}alerkin approximations of linear wave equations},
  year      = {2014},
  month     = {sep},
  number    = {3},
  pages     = {237--259},
  volume    = {95},
  doi       = {10.1002/zamm.201300306},
  publisher = {Wiley},
}

@article{arnold2002unified,
  author  = {Arnold, D. and Brezzi, F. and Cockburn, B. and Marini, L.},
  journal = {SIAM Journal on Numerical Analysis},
  title   = {Unified analysis of discontinuous {Galerkin} methods for elliptic problems},
  year    = {2002},
  number  = {5},
  pages   = {1749-1779},
  volume  = {39},
  doi     = {10.1137/S0036142901384162},
  eprint  = {https://doi.org/10.1137/S0036142901384162},
}

@article{nguyen2011high,
  author   = {N.C. Nguyen and J. Peraire and B. Cockburn},
  journal  = {Journal of Computational Physics},
  title    = {High-order implicit hybridizable discontinuous {G}alerkin methods for acoustics and elastodynamics},
  year     = {2011},
  issn     = {0021-9991},
  number   = {10},
  pages    = {3695 - 3718},
  volume   = {230},
  doi      = {https://doi.org/10.1016/j.jcp.2011.01.035},
}

@article{bangerth2010adaptive,
  author    = {W. Bangerth and M. Geiger and R. Rannacher},
  journal   = {Computational Methods in Applied Mathematics},
  title     = {Adaptive {G}alerkin finite element methods for the wave equation},
  year      = {2010},
  number    = {1},
  pages     = {3--48},
  volume    = {10},
  doi       = {10.2478/cmam-2010-0001},
  publisher = {Walter de Gruyter {GmbH}},
}

@article{duerrwaechter2021an,
  author    = {Jakob Dürrwächter and Marius Kurz and Patrick Kopper and Daniel Kempf and Claus-Dieter Munz and Andrea Beck},
  journal   = {Computers \& Fluids},
  title     = {An efficient sliding mesh interface method for high-order discontinuous {G}alerkin schemes},
  year      = {2021},
  month     = {mar},
  pages     = {104825},
  volume    = {217},
  doi       = {10.1016/j.compfluid.2020.104825},
  publisher = {Elsevier {BV}},
}


%-------------------------------------------------------------------------------
% References used elsewhere
%-------------------------------------------------------------------------------

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@techreport{Saad1991,
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