Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow
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- by W. Dörfler and M. Ainsworth;
- Math. Comp. 74 (2005), 1599-1619
- DOI: https://doi.org/10.1090/S0025-5718-05-01743-6
- Published electronically: January 3, 2005
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Abstract:
We derive computable a posteriori error estimates for the lowest order nonconforming Crouzeix–Raviart element applied to the approximation of incompressible Stokes flow. The estimator provides an explicit upper bound that is free of any unknown constants, provided that a reasonable lower bound for the inf-sup constant of the underlying problem is available. In addition, it is shown that the estimator provides an equivalent lower bound on the error up to a generic constant.References
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Bibliographic Information
- W. Dörfler
- Affiliation: Institut für Angewandte Mathematik II, Univ. Karlsruhe, 76128 Karlsruhe, Germany
- Email: doerfler@mathematik.uni-karlsruhe.de
- M. Ainsworth
- Affiliation: Department of Mathematics, Strathclyde University, 26 Richmond St., Glasgow G1 1XH, Scotland
- MR Author ID: 261514
- Email: M.Ainsworth@strath.ac.uk
- Received by editor(s): November 17, 2003
- Received by editor(s) in revised form: August 7, 2004
- Published electronically: January 3, 2005
- Additional Notes: This work was initiated during the authors’ visit to the Newton Institute for Mathematical Sciences in Cambridge. The support of the second author by the Leverhulme Trust under a Leverhulme Trust Fellowship is gratefully acknowledged.
- © Copyright 2005 American Mathematical Society
- Journal: Math. Comp. 74 (2005), 1599-1619
- MSC (2000): Primary 65N12, 65N15, 65N30
- DOI: https://doi.org/10.1090/S0025-5718-05-01743-6
- MathSciNet review: 2164088