Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: classical solutions

Abstract

We propose a new variational formulation of the elliptic Monge-Ampere equation and show how classical Lagrange elements can be used for the numerical resolution of classical solutions of the equation. Error estimates are given for Lagrange elements of degree d >= 2 in dimensions 2 and 3. No jump term is used in the variational formulation. We propose to solve the discrete nonlinear system of equations by a time marching method and numerical evidence is given which indicates that one approximates weak solutions in two dimensions.

arXiv commentThis article has been published online by IMA Journal of Numerical Analysis on May 30, 2014, doi: 10.1093/imanum/dru028. The link to the final version of the paper is: http://imajna.oxfordjournals.org/content/early/2014/05/30/imanum.dru028.abstract