% ---------------------------------------------------------------------------
% Reference collection for the student project
%   "Mean curvature computation in unfitted finite element methods"
% Computational PDEs working group, University of Goettingen.
%
% This file is meant as a starting point for the project. Feel free to extend
% it. Group publications are also listed on
%   https://cpde.math.uni-goettingen.de/publications.html
% ---------------------------------------------------------------------------

% --- Variational / distributional curvature framework (Gopalakrishnan et al.) ---

@article{GNSW_SMAIJCM_2023,
  author  = {Gopalakrishnan, Jay and Neunteufel, Michael and Sch\"oberl, Joachim and Wardetzky, Max},
  title   = {Analysis of curvature approximations via covariant curl and incompatibility for {Regge} metrics},
  journal = {The SMAI Journal of Computational Mathematics},
  volume  = {9},
  pages   = {151--195},
  year    = {2023},
  doi     = {10.5802/smai-jcm.98},
  url     = {https://doi.org/10.5802/smai-jcm.98},
}

@article{GNSW_RAM_2024,
  author  = {Gopalakrishnan, Jay and Neunteufel, Michael and Sch\"oberl, Joachim and Wardetzky, Max},
  title   = {On the improved convergence of lifted distributional {Gauss} curvature from {Regge} elements},
  journal = {Results in Applied Mathematics},
  volume  = {23},
  pages   = {100474},
  year    = {2024},
  doi     = {10.1016/j.rinam.2024.100474},
  eprint  = {2401.12734},
  url     = {https://arxiv.org/abs/2401.12734},
}

@article{GN_scalarcurv_2023,
  author  = {Gawlik, Evan S. and Neunteufel, Michael},
  title   = {Finite element approximation of scalar curvature in arbitrary dimension},
  journal = {Mathematics of Computation},
  year    = {2025},
  note    = {Preprint arXiv:2301.02159 (2023)},
  eprint  = {2301.02159},
  url     = {https://arxiv.org/abs/2301.02159},
}

% --- Weak mean-curvature vector via stabilized cut FEM (Hansbo-Larson-Zahedi) ---

@article{HLZ_SINUM_2015,
  author  = {Hansbo, Peter and Larson, Mats G. and Zahedi, Sara},
  title   = {Stabilized finite element approximation of the mean curvature vector on closed surfaces},
  journal = {SIAM Journal on Numerical Analysis},
  volume  = {53},
  number  = {4},
  pages   = {1806--1832},
  year    = {2015},
  doi     = {10.1137/140982696},
  eprint  = {1407.3043},
  url     = {https://arxiv.org/abs/1407.3043},
}

% --- Trace FEM and volume-normal-derivative (ghost-penalty) stabilization ---

@article{ORG_SINUM_2009,
  author  = {Olshanskii, Maxim A. and Reusken, Arnold and Grande, J\"org},
  title   = {A finite element method for elliptic equations on surfaces},
  journal = {SIAM Journal on Numerical Analysis},
  volume  = {47},
  number  = {5},
  pages   = {3339--3358},
  year    = {2009},
  doi     = {10.1137/080717602},
}

@article{GLR_SINUM_2018,
  author  = {Grande, J\"org and Lehrenfeld, Christoph and Reusken, Arnold},
  title   = {Analysis of a high-order trace finite element method for {PDE}s on level set surfaces},
  journal = {SIAM Journal on Numerical Analysis},
  volume  = {56},
  number  = {1},
  pages   = {228--255},
  year    = {2018},
  doi     = {10.1137/16M1102203},
}

% --- Hellan-Herrmann-Johnson mixed elements (used in the GNSW framework) ---

@article{Johnson_NM_1973,
  author  = {Johnson, Claes},
  title   = {On the convergence of a mixed finite element method for plate bending problems},
  journal = {Numerische Mathematik},
  volume  = {21},
  pages   = {43--62},
  year    = {1973},
  doi     = {10.1007/BF01436186},
}

% --- Isoparametric unfitted FEM for level-set geometries (group) ---

@article{L_CMAME_2016,
  author  = {Lehrenfeld, Christoph},
  title   = {High order unfitted finite element methods on level set domains using isoparametric mappings},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume  = {300},
  pages   = {716--733},
  year    = {2016},
  doi     = {10.1016/j.cma.2015.12.005},
  eprint  = {1509.02762},
  url     = {https://arxiv.org/abs/1509.02762},
}

% --- Higher-order curvature / geometric flow in unfitted FEM (group) ---

@phdthesis{YL_PHD_2023,
  author  = {Lou, Yimin},
  title   = {High-order Unfitted Discretizations for Partial Differential Equations Coupled with Geometric Flow},
  school  = {University of G\"ottingen},
  year    = {2023},
  url     = {http://dx.doi.org/10.53846/goediss-9736},
}