Two-scale method for the Monge-Ampère Equation: Pointwise Error Estimates

Abstract

In this paper we continue the analysis of the two-scale method for the Monge-Ampère equation for dimension $d\ge 2$ introduced in [10]. We prove continuous dependence of discrete solutions on data that in turn hinges on a discrete version of the Alexandroff estimate. They are both instrumental to prove pointwise error estimates for classical solutions with Hölder and Sobolev regularity. We also derive convergence rates for viscosity solutions with bounded Hessians which may be piecewise smooth or degenerate.

21 pages, accepted in IMA Journal of Numerical Analysis

References in corpus (2)

• Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Ampère equation
• Convergent semi-Lagrangian methods for the Monge-Ampère equation on unstructured grids

Cited by in corpus (2)

• Convergent filtered scheme for the Monge-Ampère Equation
• Two-Scale Method for the Monge-Ampère Equation: Convergence to the Viscosity Solution