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Local and pointwise error estimates of the local discontinuous Galerkin method applied to the Stokes problem


Author: J. Guzmán
Journal: Math. Comp. 77 (2008), 1293-1322
MSC (2000): Primary 65N30, 65N15
Published electronically: January 25, 2008
MathSciNet review: 2398769
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Abstract: We prove local and pointwise error estimates for the local discontinuous Galerkin method applied to the Stokes problem in two and three dimensions. By using techniques originally developed by A. Schatz [Math. Comp., 67 (1998), 877-899] to prove pointwise estimates for the Laplace equation, we prove optimal weighted pointwise estimates for both the velocity and the pressure for domains with smooth boundaries.


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Additional Information

J. Guzmán
Affiliation: School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, Minnesota 55455
Email: guzma033@umn.edu

DOI: https://doi.org/10.1090/S0025-5718-08-02067-X
Keywords: Finite elements, discontinuous Galerkin, Stokes problem
Received by editor(s): September 26, 2006
Received by editor(s) in revised form: April 30, 2007
Published electronically: January 25, 2008
Additional Notes: The author was supported by a National Science Foundation Mathematical Science Postdoctoral Research Fellowship (DMS-0503050)
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.