A noncoforming virtual element approximation for the Oseen eigenvalue problem

TL;DR

This paper introduces a nonconforming virtual element method for accurately approximating eigenvalues and eigenfunctions of the 2D Oseen eigenvalue problem, ensuring divergence-free solutions and optimal convergence.

Contribution

It develops a divergence-free virtual element approach with proven convergence and double order spectral accuracy for the Oseen eigenvalue problem.

Findings

Method achieves divergence-free eigenfunctions.

Convergence and error estimates are established.

Numerical tests confirm theoretical results.

Abstract

In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is capable to capture properly the divergence at discrete level and the eigenvalues and eigenfunctions. Under the compact theory for operators we prove convergence and error estimates for the method. By employing the theory of compact operators we recover the double order of convergence of the spectrum. Finally, we present numerical tests to assess the performance of the proposed numerical scheme.