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.
Keywords
Cite
@article{arxiv.1310.4576,
title = {Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: classical solutions},
author = {Gerard Awanou},
journal= {arXiv preprint arXiv:1310.4576},
year = {2015}
}
Comments
This 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