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Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow


Authors: W. Dörfler and M. Ainsworth
Journal: Math. Comp. 74 (2005), 1599-1619
MSC (2000): Primary 65N12, 65N15, 65N30
DOI: https://doi.org/10.1090/S0025-5718-05-01743-6
Published electronically: January 3, 2005
MathSciNet review: 2164088
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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.


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Additional 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

Keywords: Computable error bounds, a posteriori error estimates, nonconforming finite elements, Stokes flow.
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.
Article copyright: © Copyright 2005 American Mathematical Society