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arXiv · 1712.06816

Arnold-Winther mixed finite elements for Stokes eigenvalue problems

Joscha Gedicke·Arbaz Khan
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Abstract

This paper is devoted to study the Arnold-Winther mixed finite element method for two dimensional Stokes eigenvalue problems using the stress-velocity formulation. A priori error estimates for the eigenvalue and eigenfunction errors are presented. To improve the approximation for both eigenvalues and eigenfunctions, we propose a local post-processing. With the help of the local post-processing, we derive a reliable a posteriori error estimator which is shown to be empirically efficient. We confirm numerically the proven higher order convergence of the post-processed eigenvalues for convex domains with smooth eigenfunctions. On adaptively refined meshes we obtain numerically optimal higher orders of convergence of the post-processed eigenvalues even on nonconvex domains.

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Joscha Gedicke, Arbaz Khan. 2017-12-19. Arnold-Winther mixed finite elements for Stokes eigenvalue problems. https://arxiv.org/abs/1712.06816

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