Geodesic
Finite element approximations of the three dimensional Monge-Ampère equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 979-1001

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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.

DOI : 10.1051/m2an/2011067
Classification : 65N30, 35J60
Keywords: Monge-Ampère equation, three dimensions, finite element method, convergence analysis 
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     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},
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     year = {2012},
     doi = {10.1051/m2an/2011067},
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     zbl = {1272.65088},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011067/}
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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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