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Supercloseness and superconvergence of stabilized low-order finite element discretizations of the Stokes Problem


Authors: Hagen Eichel, Lutz Tobiska and Hehu Xie
Journal: Math. Comp. 80 (2011), 697-722
MSC (2010): Primary 65N30; Secondary 76D07
DOI: https://doi.org/10.1090/S0025-5718-2010-02404-4
Published electronically: August 20, 2010
MathSciNet review: 2772093
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Abstract: The supercloseness and superconvergence properties of stabilized finite element methods applied to the Stokes problem are studied. We consider consistent residual based stabilization methods as well as inconsistent local projection type stabilizations. Moreover, we are able to show the supercloseness of the linear part of the MINI-element solution which has been previously observed in practical computations. The results on supercloseness hold on three-directional triangular, axiparallel rectangular, and brick-type meshes, respectively, but extensions to more general meshes are also discussed. Applying an appropriate postprocess to the computed solution, we establish superconvergence results. Numerical examples illustrate the theoretical predictions.


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Additional Information

Hagen Eichel
Affiliation: Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
Email: hagen.eichel@st.ovgu.de

Lutz Tobiska
Affiliation: Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
Email: tobiska@ovgu.de

Hehu Xie
Affiliation: LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Address at time of publication: Institute for Analysis and Computational Mathematics, Otto-von-Guericke University Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
Email: hhxie@lsec.cc.ac.cn

DOI: https://doi.org/10.1090/S0025-5718-2010-02404-4
Received by editor(s): August 3, 2009
Received by editor(s) in revised form: December 10, 2009
Published electronically: August 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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