Quadratic Mixed finite element approximations of the Monge-Ampere equation in 2D

TL;DR

This paper presents error estimates for a quadratic mixed finite element method applied to the 2D Monge-Ampere equation, focusing on approximating the scalar variable and Hessian matrix using degree two Lagrange elements.

Contribution

It provides the first detailed error analysis for a quadratic mixed finite element approach to the 2D Monge-Ampere equation.

Findings

Error estimates established for the quadratic mixed finite element method.

The method effectively approximates both the scalar variable and Hessian matrix.

Theoretical convergence rates are demonstrated.

Abstract

We give error estimates for a mixed finite element approximation of the two-dimensional elliptic Monge-Ampere equation with the unknowns approximated by Lagrange finite elements of degree two. The variables in the formulation are the scalar variable and the Hessian matrix.