In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.
Mots clés : Monge-Ampère equation, three dimensions, finite element method, convergence analysis
@article{M2AN_2012__46_5_979_0, author = {Brenner, Susanne Cecelia and Neilan, Michael}, title = {Finite element approximations of the three dimensional {Monge-Amp\`ere} equation}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {979--1001}, publisher = {EDP-Sciences}, volume = {46}, number = {5}, year = {2012}, doi = {10.1051/m2an/2011067}, mrnumber = {2916369}, zbl = {1272.65088}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2011067/} }
TY - JOUR AU - Brenner, Susanne Cecelia AU - Neilan, Michael TI - Finite element approximations of the three dimensional Monge-Ampère equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 979 EP - 1001 VL - 46 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011067/ DO - 10.1051/m2an/2011067 LA - en ID - M2AN_2012__46_5_979_0 ER -
%0 Journal Article %A Brenner, Susanne Cecelia %A Neilan, Michael %T Finite element approximations of the three dimensional Monge-Ampère equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 979-1001 %V 46 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011067/ %R 10.1051/m2an/2011067 %G en %F M2AN_2012__46_5_979_0
Brenner, Susanne Cecelia; Neilan, Michael. Finite element approximations of the three dimensional Monge-Ampère equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 979-1001. doi : 10.1051/m2an/2011067. http://www.numdam.org/articles/10.1051/m2an/2011067/
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