Guaranteed error control for the pseudostress approximation of the Stokes equations

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Date
2015
Volume
2106
Issue
Journal
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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.

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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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