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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
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
Email: M.Ainsworth@strath.ac.uk

DOI: http://dx.doi.org/10.1090/S0025-5718-05-01743-6
PII: S 0025-5718(05)01743-6
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