Gedicke, Joscha and Khan, Arbaz (2017) Arnold-Winther Mixed Finite Elements for Stokes Eigenvalue Problems. [MIMS Preprint]
PDF
GK_AW_Stokes_preprint.pdf Download (1MB) |
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: | https://eprints.maths.manchester.ac.uk/id/eprint/2564 |
Actions (login required)
View Item |