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

TL;DR

This paper proves the convergence of a hybrid numerical scheme combining finite difference and monotone methods to solve the elliptic Monge-Ampere equation, addressing solver limitations.

Contribution

It introduces a hybrid discretization approach that ensures convergence to the viscosity solution of the Monge-Ampere equation.

Findings

Hybrid scheme converges to the viscosity solution.

Combines standard finite difference and monotone schemes effectively.

Addresses solver issues for standard discretization.

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.