Stability and interpolation estimates of Hellinger-Reissner virtual element spaces

TL;DR

This paper establishes stability and interpolation estimates for Hellinger-Reissner virtual elements, showing that constants depend only on shape quality and accuracy degree, with numerical analysis on challenging geometries.

Contribution

It provides the first stability and interpolation estimates for Hellinger-Reissner virtual elements with constants depending solely on shape and accuracy.

Findings

Constants depend only on aspect ratio and scheme degree

Numerical behavior analyzed on badly-shaped polytopes

Stability estimates verified for high accuracy levels

Abstract

We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope under consideration and the degree of accuracy of the scheme. We further investigate numerically the behaviour of the constants appearing in the stability estimates on sequences of badly-shaped polytopes and for increasing degree of accuracy.