Adaptive mixed FEM for the Stokes eigenvalue problem

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.

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Publication Details

Journal
Mathematics of Computation
Published
2025-12-01
DOI
https://doi.org/10.1090/mcom/4151
Primary Topic
Advanced Numerical Methods in Computational Mathematics
Type
article
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article

Adaptive mixed FEM for the Stokes eigenvalue problem

Arbaz Khan, Daniele Boffi
Mathematics of Computation
Advanced Numerical Methods in Computational Mathematics
article

Adaptive mixed FEM for the Stokes eigenvalue problem

Arbaz Khan, Daniele Boffi
article en

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.

Mathematics of Computation
Indian Institute of Technology Roorkee (IN), University of Pavia (IT), King Abdullah University of Science and Technology (SA)
Openalex Percentile: Top 61%
Advanced Numerical Methods in Computational Mathematics
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