The Mixed Virtual Element Discretization for highly-anisotropic problems: the role of the boundary degrees of freedom

TL;DR

This paper evaluates the accuracy and robustness of mixed Virtual Element Methods for highly-anisotropic diffusion problems, introducing a new boundary degrees of freedom definition and comparing different approaches.

Contribution

It proposes a novel boundary degrees of freedom definition and analyzes various mixed Virtual Element approaches for anisotropic problems.

Findings

The new boundary degrees of freedom improves accuracy.

Different approaches show varying robustness under anisotropy.

The method performs well with both constant and variable coefficients.

Abstract

In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly-anisotropic diffusion problems. In particular, we analyze the performances of different approaches which are characterized by different sets of both boundary and internal degrees of freedom in presence of a strong anisotropy of the diffusion tensor with constant or variable coefficients. A new definition of the boundary degrees of freedom is also proposed and tested.