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ARNOLD-WINTHER MIXED FINITE ELEMENTS FOR STOKES EIGENVALUE PROBLEMS
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DOI：10.1137/17M1162032.png)
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摘要
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This paper is devoted to studying 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 postprocessing. With the help of the local postprocessing, 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 postprocessed eigenvalues for convex domains with smooth eigenfunctions. On adaptively refined meshes we obtain numerically optimal higher orders of convergence of the postprocessed eigenvalues even on nonconvex domains.
Keyword:
priori analysis
a posteriori analysis
Arnold-Winther finite element
mixed finite element
Stokes eigenvalue problem
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被引数:
1.8W
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