Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes

TL;DR

This paper introduces a mixed Virtual Element Method for solving general second order elliptic problems on polygonal meshes, providing theoretical convergence analysis and numerical validation.

Contribution

It develops a novel VEM approach for mixed elliptic problems with variable coefficients, including convergence proofs and numerical tests.

Findings

The method achieves optimal convergence rates.

Numerical tests confirm theoretical predictions.

Applicable to complex polygonal meshes.

Abstract

In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis of the method and develop a set of numerical tests on a benchmark problem with known solution.