Spline element method for the Monge-Ampere equation

Abstract

We analyze the convergence of an iterative method for solving the nonlinear system resulting from a natural discretization of the Monge-Ampère equation with $C^1$ conforming approximations. We make the assumption, supported by numerical experiments for the two dimensional problem, that the discrete problem has a convex solution. The method we analyze is the discrete version of Newton's method in the vanishing moment methodology. Numerical experiments are given in the framework of the spline element method.

References in corpus (2)

• A finite element method for fully nonlinear elliptic problems
• The Monge-Ampere equation: various forms and numerical methods

Cited by in corpus (1)

• Pseudo transient continuation and time marching methods for Monge-Ampere type equations