Guaranteed error control for the pseudostress approximation of the Stokes equations

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Date
2015
Volume
2106
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

The pseudostress approximation of the Stokes equations rewrites the stationary Stokes equations with pure (but possibly inhomogeneous) Dirichlet boundary conditions as another (equivalent) mixed scheme based on a stress in H (div) and the velocity in L2. Any standard mixed finite element function space can be utilized for this mixed formulation, e.g. the Raviart-Thomas discretization which is related to the Crouzeix-Raviart nonconforming finite element scheme in the lowest-order case. The effective and guaranteed a posteriori error control for this nonconforming velocity-oriented discretization can be generalized to the error control of some piecewise quadratic velocity approximation that is related to the discrete pseudostress. The analysis allows for local inf-sup constants which can be chosen in a global partition to improve the estimation. Numerical examples provide strong evidence for an effective and guaranteed error control with very small overestimation factors even for domains with large anisotropy.

Description
Keywords
Nonconforming finite element method, Crouzeix-Raviart element, Stokes equations, pseudostress finite element method, adaptive finite element method, a posteriori error estimation
Citation
Bringmann, P., Carstensen, C., & Merdon, C. (2015). Guaranteed error control for the pseudostress approximation of the Stokes equations (Vol. 2106). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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