references.bib

@misc{DOLFINx2023,
  author    = {Igor A. Baratta and Joseph P. Dean and Jørgen S. Dokken and Michal Habera and Jack S. Hale and Chris N. Richardson and Marie E. Rognes
               and Matthew W. Scroggs and Nathan Sime and Garth N. Wells},
  title     = {DOLFINx: The next generation FEniCS problem solving environment},
  year      = {2023},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.10447666}
}


@article{ZHANG2022Gibbs,
  title    = {{Battling Gibbs phenomenon: On finite element approximations of discontinuous solutions of PDEs}},
  journal  = {Computers & Mathematics with Applications},
  volume   = {122},
  pages    = {35--47},
  year     = {2022},
  issn     = {0898-1221},
  doi      = {10.1016/j.camwa.2022.07.014},
  author   = {Shun Zhang},
  keywords = {Discontinuous solution of PDEs, Gibbs phenomenon, Overshoot, Adaptive finite element methods, Singularly perturbed equation}
}


@book{ciarlet2002,
  author    = {Ciarlet, Philippe G.},
  title     = {The Finite Element Method for Elliptic Problems},
  publisher = {Society for Industrial and Applied Mathematics},
  year      = {2002},
  doi       = {10.1137/1.9780898719208},
  address   = {},
  edition   = {}
}

@misc{sulli2012lecture,
  title    = {Lecture notes on finite element methods for partial differential equations},
  author   = {S{\"u}li, Endre},
  year     = {2012},
  pulisher = {University of Oxford},
  url      = {https://people.maths.ox.ac.uk/suli/fem.pdf}
}


@misc{chenmaxwell,
  title     = {VARIATIONAL FORMULATION OF MAXWELL EQUATIONS},
  author    = {Chen, Long},
  publisher = {Department of Mathematics, University of California},
  url       = {https://www.math.uci.edu/~chenlong/226/Maxwellweakform.pdf}
}


@phdthesis{dean2023,
  title    = {Mathematical and computational aspects of solving mixed-domain problems using the finite element method},
  url      = {https://www.repository.cam.ac.uk/handle/1810/367855},
  doi      = {10.17863/CAM.108292},
  school   = {Apollo - University of Cambridge Repository},
  author   = {Dean, Joseph},
  year     = {2023},
  keywords = {Finite element analysis, High-performance computing, Mixed-domain problems, Multiphysics problems, Partial differential equations, Structure-preserving methods}
}


@misc{keith2024,
  title         = {Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints},
  author        = {Brendan Keith and Thomas M. Surowiec},
  year          = {2024},
  eprint        = {2307.12444},
  archiveprefix = {arXiv},
  primaryclass  = {math.NA},
  url           = {https://arxiv.org/abs/2307.12444}
}

@misc{dokken2024,
  title     = {The latent variable proximal point algorithm for problems with pointwise constraints},
  author    = {Dokken, J.S. and Farrell P.E. and Keith, B. and Surowiec, T.M.},
  publisher = {In preparation},
  year      = {2024}
}