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. © EDP Sciences, SMAI, 2012.
Publication Source (Journal or Book title)
ESAIM: Mathematical Modelling and Numerical Analysis
Brenner, S., & Neilan, M. (2012). Finite element approximations of the three dimensional Monge-Ampère equation. ESAIM: Mathematical Modelling and Numerical Analysis, 46 (5), 979-1001. https://doi.org/10.1051/m2an/2011067