Nonconforming virtual element method for general second-order elliptic problems on curved domain

TL;DR

This paper develops a nonconforming virtual element method for second-order elliptic problems on curved domains, achieving optimal convergence rates and demonstrating accuracy through numerical experiments on polygonal meshes.

Contribution

It introduces a novel nonconforming virtual element approach tailored for curved domains with variable coefficients, with proven optimal convergence.

Findings

Optimal convergence in energy and L2 norms

Numerical experiments confirm theoretical accuracy

Method performs well on polygonal meshes

Abstract

This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal convergence in the energy and $L^2$ norms, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the method is shown to be comparable with the theoretical analysis.