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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0025-5718-05-01743-6
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
