Convergence of a hybrid scheme for the elliptic Monge-Ampere equation

Abstract

We prove the convergence of a hybrid discretization to the viscosity solution of the elliptic Monge-Ampere equation. The hybrid discretization uses a standard finite difference discretization in parts of the computational domain where the solution is expected to be smooth and a monotone scheme elsewhere. A motivation for the hybrid discretization is the lack of an appropriate Newton solver for the standard finite difference discretization on the whole domain.

References in corpus (4)

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• On standard finite difference discretizations of the elliptic Monge-Ampere equation
• A variational method for computing numerical solutions of the Monge-Ampere equation