Postprocessing and Higher Order Convergence of Stabilized Finite Element Discretizations of the Stokes Eigenvalue Problem

TL;DR

This paper applies stabilized finite element methods to the Stokes eigenvalue problem, introduces a postprocessing technique to enhance convergence rates, and confirms theoretical results with numerical examples.

Contribution

It presents a novel postprocessing strategy that improves eigenpair convergence for stabilized finite element discretizations of the Stokes problem.

Findings

Enhanced convergence rates through postprocessing

Numerical validation of theoretical convergence improvements

Effective stabilization in finite element discretizations

Abstract

In this paper, the stabilized finite element method based on local projection is applied to discretize the Stokes eigenvalue problems and the corresponding convergence analysis is given. Furthermore, we also use a method to improve the convergence rate for the eigenpair approximations of the Stokes eigenvalue problem. It is based on a postprocessing strategy that contains solving an additional Stokes source problem on an augmented finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order of mixed finite element space. Numerical examples are given to confirm the theoretical analysis.