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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.
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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
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