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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

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

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.