Adaptive Mixed FEM for the Stokes eigenvalue problem

TL;DR

This paper develops and analyzes an adaptive mixed finite element method for solving the Stokes eigenvalue problem, demonstrating optimal convergence and confirming effectiveness through numerical experiments.

Contribution

It provides the first rigorous proof of quasi-orthogonality and discrete reliability for this adaptive scheme applied to the Stokes eigenvalue problem.

Findings

Optimal convergence of the adaptive scheme is established.

Numerical experiments confirm the scheme's efficiency.

The method outperforms non-adaptive approaches.

Abstract

In this paper we discuss the optimal convergence of a standard adaptive scheme based on mixed finite element approximation to the solution of the eigenvalue problem associated with the Stokes equations. The proofs of the quasi-orthogonality and the discrete reliability are presented. Our numerical experiments confirm the efficacy of the proposed adaptive scheme.