A high order stabilization-free virtual element method for general second-order elliptic eigenvalue problem

TL;DR

This paper introduces a higher-order virtual element method for second-order elliptic eigenvalue problems that does not require stabilization, providing optimal error estimates and validated by numerical experiments on various polygonal meshes.

Contribution

The paper presents a novel stabilization-free virtual element method with optimal error estimates for general second-order elliptic eigenvalue problems.

Findings

Achieved optimal a priori error estimates for eigenspaces and eigenvalues.

Validated the method's effectiveness through numerical experiments on diverse polygonal meshes.

Abstract

In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are derived for both the approximate eigenspace and eigenvalues. Numerical experiments are conducted on regular convex polygonal meshes, convex-concave polygonal meshes, and concave polygonal meshes. The numerical results validate the effectiveness of the proposed method.