Finite element approximations of the three dimensional Monge-Ampère equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, p. 979-1001

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.

DOI : https://doi.org/10.1051/m2an/2011067
Classification:  65N30,  35J60
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {5},
     year = {2012},
     pages = {979-1001},
     doi = {10.1051/m2an/2011067},
     zbl = {1272.65088},
     mrnumber = {2916369},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, pp. 979-1001. doi : 10.1051/m2an/2011067. http://www.numdam.org/item/M2AN_2012__46_5_979_0/

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