Work

A nonlinear least-squares convexity enforcing 𝐶⁰ interior penalty method for the Monge–Ampère equation on strictly convex smooth planar domains

Year: 2024

Type: article

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 R 2 {\mathbb {R}}^2 . It is based on an isoparametric C 0 C^0 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.

Source: Communications of the American Mathematical Society

DOI: 10.1090/cams/39

Authors: Susanne Brenner, Li-yeng Sung, Zhiyu Tan, Hongchao Zhang

Institutions: Louisiana State University, Xiamen University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Science Foundation, Fundamental Research Funds for the Central Universities