Virtual element methods for a quad-curl problem on general planar domains

TL;DR

This paper develops virtual element methods for solving quad-curl problems on general polygonal domains, utilizing Hodge decomposition, with numerical results supporting the theoretical findings.

Contribution

It introduces a novel virtual element approach for quad-curl problems on arbitrary polygonal domains based on Hodge decomposition.

Findings

The methods are theoretically sound and converge as expected.

Numerical experiments confirm the effectiveness of the proposed methods.

Abstract

We design and analyze virtual element methods for a quad-curl problem on general polygonal domains that are based on the Hodge decomposition of divergence-free vector fields. Numerical results that corroborate the theoretical analysis are also presented.