Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra
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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.References
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Additional Information
- J. Guzmán
- Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02906
- MR Author ID: 775211
- Email: Johnny_Guzman@brown.edu
- D. Leykekhman
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- MR Author ID: 680657
- Email: leykekhman@math.uconn.edu
- 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. - © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1879-1902
- MSC (2010): Primary 65N30, 65N15
- DOI: https://doi.org/10.1090/S0025-5718-2012-02603-2
- MathSciNet review: 2945141