Finite element approximations of the three dimensional Monge-Ampère equation

Brenner, Susanne Cecelia; Neilan, Michael

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 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.

Classification : 65N30, 35J60
Mots clés : Monge-Ampère equation, three dimensions, finite element method, convergence analysis

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