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A posteriori FE error control for p-Laplacian by gradient recovery in quasi-norm


Authors: Carsten Carstensen, W. Liu and N. Yan
Journal: Math. Comp. 75 (2006), 1599-1616
MSC (2000): Primary 65N30, 49J40
DOI: https://doi.org/10.1090/S0025-5718-06-01819-9
Published electronically: June 7, 2006
MathSciNet review: 2240626
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Abstract: A posteriori error estimators based on quasi-norm gradient recovery are established for the finite element approximation of the p-Laplacian on unstructured meshes. The new a posteriori error estimators provide both upper and lower bounds in the quasi-norm for the discretization error. The main tools for the proofs of reliability are approximation error estimates for a local approximation operator in the quasi-norm.


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Additional Information

Carsten Carstensen
Affiliation: Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
Email: cc@math.hu-berlin.de

W. Liu
Affiliation: CBS & Institute of Mathematics and Statistics, University of Kent, Canterbury, CT2 7NF, England
Email: W.B.Liu@ukc.ac.uk

N. Yan
Affiliation: Institute of System Sciences, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, People’s Republic of China
Email: yan@amss.ac.cn

DOI: https://doi.org/10.1090/S0025-5718-06-01819-9
Keywords: Finite element approximation, p-Laplacian, a posteriori error estimators, gradient recovery, quasi-norm error bounds
Received by editor(s): April 16, 2003
Received by editor(s) in revised form: May 3, 2005
Published electronically: June 7, 2006
Additional Notes: Supported by the DFG Research Center MATHEON “Mathematics for key technologies” in Berlin.
Article copyright: © Copyright 2006 American Mathematical Society