A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator

TL;DR

This paper develops an a priori error analysis for a mixed virtual element method applied to the Laplacian eigenvalue problem, demonstrating convergence, optimal error estimates, and confirming results through numerical tests.

Contribution

It introduces a new error analysis framework for a mixed VEM discretization of the Laplacian eigenproblem, ensuring spurious-free and convergent solutions.

Findings

Method is spurious free and convergent.

Achieves optimal order error estimates.

Numerical tests confirm theoretical predictions.

Abstract

The aim of the present work is to derive a error estimates for the Laplace eigenvalue problem in mixed form, by means of a virtual element method. With the aid of the theory for non-compact operators, we prove that the proposed method is spurious free and convergent. We prove optimal order error estimates for the eigenvalues and eigenfunctions. Finally, we report numerical tests to confirm the theoretical results together with a rigorous computational analysis of the effects of the stabilization in the computation of the spectrum.