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2017.25: Arnold-Winther Mixed Finite Elements for Stokes Eigenvalue Problems

2017.25: Joscha Gedicke and Arbaz Khan (2017) Arnold-Winther Mixed Finite Elements for Stokes Eigenvalue Problems.

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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 2000 > 65 Numerical analysis
MIMS number:2017.25
Deposited By:Dr. Arbaz Khan
Deposited On:01 August 2017

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