Stabilization-free serendipity virtual element method for plane elasticity

TL;DR

This paper introduces a higher order, stabilization-free virtual element method for plane elasticity that reduces degrees of freedom and achieves optimal convergence rates, validated through numerical eigenanalysis and benchmark tests.

Contribution

It presents a novel serendipity virtual element method that is stabilization-free and reduces degrees of freedom for plane elasticity problems.

Findings

Achieves optimal convergence rates in $L^2$ and energy seminorms.

Validated through numerical eigenanalysis and benchmark problems.

Matches theoretical estimates and higher order virtual element methods.

Abstract

We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations. The well-posedness of the problem is numerically studied via an eigenanalysis. The method is then applied to several benchmark problems from linear elasticity and we show that the method delivers optimal convergence rates in $L^2$ norm and energy seminorm that match theoretical estimates as well as the convergence rates from higher order virtual element methods.