RESIDUAL-BASED A POSTERIORI ERROR ESTIMATES FOR A CONFORMING MIXED FINITE ELEMENT DISCRETIZATION OF THE MONGE-AMPÈRE EQUATION

Abstract

In this paper we develop a new a posteriori error analysis for the Monge-Ampère equation approximated by conforming finite element method on isotropic meshes in R 2 . The approach utilizes a slight variant of the mixed discretization proposed by Gérard Awanou and Hengguang Li in [4]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.