Arnold-Winther Mixed Finite Elements for Stokes Eigenvalue Problems

Gedicke, Joscha and Khan, Arbaz (2017) Arnold-Winther Mixed Finite Elements for Stokes Eigenvalue Problems. [MIMS Preprint]

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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.

Item Type: MIMS Preprint
Uncontrolled Keywords: a priori analysis, a posteriori analysis, Arnold-Winther finite element, mixed finite element, Stokes eigenvalue problem
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Arbaz Khan
Date Deposited: 01 Aug 2017
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2564

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