The Virtual Element Method for a Minimal Surface Problem

TL;DR

This paper introduces a Virtual Element Method for solving a minimal surface problem modeled by a quasi-linear elliptic PDE, providing optimal error estimates and validating them through numerical experiments.

Contribution

The paper develops a novel Virtual Element discretization for minimal surface problems, including rigorous error analysis and numerical validation.

Findings

Optimal error estimates derived for the VEM scheme

Numerical tests confirm theoretical convergence rates

Method effectively approximates minimal surface solutions

Abstract

In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We derive optimal error estimate and present several numerical tests assessing the validity of the theoretical results.