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

 

Local pointwise a posteriori gradient error bounds for the Stokes equations


Authors: Alan Demlow and Stig Larsson
Journal: Math. Comp. 82 (2013), 625-649
MSC (2010): Primary 65N30
Published electronically: November 27, 2012
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Abstract: We consider the standard Taylor-Hood finite element method for the stationary Stokes system on polyhedral domains. We prove local a posteriori error estimates for the maximum error in the gradient of the velocity field. Because the gradient of the velocity field blows up near reentrant corners and edges, such local error control is necessary when pointwise control of the gradient error is desirable. Computational examples confirm the utility of our estimates in adaptive codes.


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Additional Information

Alan Demlow
Affiliation: Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506
Email: alan.demlow@uky.edu

Stig Larsson
Affiliation: Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE–412 96 Gothenburg, Sweden
Email: stig@chalmers.se

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02647-0
PII: S 0025-5718(2012)02647-0
Keywords: Stokes system, Taylor-Hood, finite element, a posteriori, gradient, local
Received by editor(s): May 10, 2010
Received by editor(s) in revised form: August 12, 2011
Published electronically: November 27, 2012
Additional Notes: The first author was partially supported by NSF grant DMS-0713770.
The second author was partially supported by the Swedish Research Council (VR) and by the Swedish Foundation for Strategic Research (SSF) through GMMC, the Gothenburg Mathematical Modelling Centre.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.