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Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra.


Authors: J. Guzmán and D. Leykekhman
Journal: Math. Comp. 81 (2012), 1879-1902
MSC (2010): Primary 65N30, 65N15
DOI: https://doi.org/10.1090/S0025-5718-2012-02603-2
Published electronically: March 1, 2012
MathSciNet review: 2945141
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Abstract: The aim of the paper is to show the stability of the finite element solution for the Stokes system in $ W^1_\infty $ norm on general convex polyhedral domain. In contrast to previously known results, $ W^2_r$ regularity for $ r>3$, which does not hold for general convex polyhedral domains, is not required. The argument uses recently available sharp Hölder pointwise estimates of the corresponding Green's matrix together with novel local energy error estimates, which do not involve an error of the pressure in a weaker norm.


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Additional Information

J. Guzmán
Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02906
Email: Johnny_Guzman@brown.edu

D. Leykekhman
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: leykekhman@math.uconn.edu

DOI: https://doi.org/10.1090/S0025-5718-2012-02603-2
Keywords: Maximum norm, finite element, optimal error estimates, Stokes
Received by editor(s): May 21, 2010
Received by editor(s) in revised form: May 10, 2011, and August 18, 2011
Published electronically: March 1, 2012
Additional Notes: The first author was partially supported by NSF grant DMS-0914596.
The second author was partially supported by NSF grant DMS-0811167.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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