Anisotropic finite elements for the Stokes problem: a posteriori error estimator and adaptive mesh

Authors:
Maharavo Randrianarivony
Affiliations:
Fakultät für Informatik, Technische Universität Chemnitz, Strasse der Nationen 62, Chemnitz D-09107, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

We propose an a posteriori error estimator for the Stokes problem using the Crouzeix-Raviart/P0 pair. Its efficiency and reliability on highly stretched meshes are investigated. The analysis is based on hierarchical space splitting whose main ingredients are the strengthened Cauchy-Schwarz inequality and the saturation assumption. We give a theoretical proof of a method to enrich the Crouzeix-Raviart element so that the strengthened Cauchy constant is always bounded away from unity independently of the aspect ratio. An anisotropic self-adaptive mesh refinement approach for which the saturation assumption is valid will be described. Our theory is confirmed by corroborative numerical tests which include an internal layer, a boundary layer, a re-entrant corner and a crack simulation. A comparison of the exact error and the a posteriori one with respect to the aspect ratio will be demonstrated.