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

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- by Hagen Eichel, Lutz Tobiska and Hehu Xie PDF
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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.## References

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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
- Received by editor(s): August 3, 2009
- Received by editor(s) in revised form: December 10, 2009
- Published electronically: August 20, 2010
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**80**(2011), 697-722 - MSC (2010): Primary 65N30; Secondary 76D07
- DOI: https://doi.org/10.1090/S0025-5718-2010-02404-4
- MathSciNet review: 2772093