Error Analysis of a Mixed Finite Element Method for the Monge-Ampère Equation

Abstract

We analyze the convergence of a mixed finite element method for the elliptic Monge-Ampère  equation in dimensions 2 and 3. The unknowns in the formulation, the scalar variable and a discrete Hessian, are approximated by Lagrange finite element spaces. The method originally proposed by Lakkis and Pryer can be viewed as the formal limit of a Hermann-Miyoshi mixed method proposed by Feng and Neilan in the context of the vanishing moment methodology. Error estimates are derived under the assumption that the continuous problem has a smooth solution.