A convexity enforcing C interior penalty method for the Monge–Ampère equation on convex polygonal domains

Document Type

Article

Publication Date

7-1-2021

Abstract

We design and analyze a C interior penalty method for the approximation of classical solutions of the Dirichlet boundary value problem of the Monge–Ampère equation on convex polygonal domains. The method is based on an enhanced cubic Lagrange finite element that enables the enforcement of the convexity of the approximate solutions. Numerical results that corroborate the a priori and a posteriori error estimates are presented. It is also observed from numerical experiments that this method can capture certain weak solutions.

Publication Source (Journal or Book title)

Numerische Mathematik

First Page

497

Last Page

524

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