Abstract

In two dimensions, we study a conforming inf–sup stable Virtual Element Method to approximate the eigenvalues and eigenfunctions of the Stokes eigenvalue problem. Under the framework of compact operator theory, we prove convergence of the method and derive a priori error estimates. We also design a residual-based a posteriori error estimator, which is shown to be both reliable and efficient. We present a series of numerical tests to assess the performance of the method in both a priori and a posteriori error analyses, along with a detailed study of the influence of the stabilization term on the convergence rates and the appearance of spurious eigenvalues. © 2025 Elsevier B.V.