A NONLINEAR LEAST-SQUARES CONVEXITY ENFORCING C0 INTERIOR PENALTY METHOD FOR THE MONGE–AMPÈRE EQUATION ON STRICTLY CONVEX SMOOTH PLANAR DOMAINS

Authors

Susanne C. Brenner, Louisiana State University
Li Yeng Sung, Louisiana State University
Zhiyu Tan, Louisiana State University
Hongchao Zhang, Louisiana State University

Document Type

Article

Publication Date

1-1-2024

Abstract

We construct a nonlinear least-squares finite element method for com­puting the smooth convex solutions of the Dirichlet boundary value problem of the Monge-Ampère equation on strictly convex smooth domains in R². It is based on an isoparametric C⁰ finite element space with exotic degrees of freedom that can enforce the convexity of the approximate solutions. A priori and a posteriori error estimates together with corroborating numerical results are presented.

Publication Source (Journal or Book title)

Communications of the American Mathematical Society

First Page

607

Last Page

640

Recommended Citation

Brenner, S., Sung, L., Tan, Z., & Zhang, H. (2024). A NONLINEAR LEAST-SQUARES CONVEXITY ENFORCING C0 INTERIOR PENALTY METHOD FOR THE MONGE–AMPÈRE EQUATION ON STRICTLY CONVEX SMOOTH PLANAR DOMAINS. Communications of the American Mathematical Society, 4, 607-640. https://doi.org/10.1090/cams/39