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The local discontinuous Galerkin method for the Oseen equations

Authors: Bernardo Cockburn, Guido Kanschat and Dominik Schötzau
Journal: Math. Comp. 73 (2004), 569-593
MSC (2000): Primary 65N30
Published electronically: May 21, 2003
MathSciNet review: 2031395
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Abstract: We introduce and analyze the local discontinuous Galerkin method for the Oseen equations of incompressible fluid flow. For a class of shape-regular meshes with hanging nodes, we derive optimal a priori estimates for the errors in the velocity and the pressure in $L^2$- and negative-order norms. Numerical experiments are presented which verify these theoretical results and show that the method performs well for a wide range of Reynolds numbers.

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Additional Information

Bernardo Cockburn
Affiliation: School of Mathematics, University of Minnesota, Vincent Hall, Minneapolis, Minnesota 55455

Guido Kanschat
Affiliation: Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293/294, 69120 Heidelberg, Germany

Dominik Schötzau
Affiliation: Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland

Keywords: Finite elements, discontinuous Galerkin methods, Oseen equations
Received by editor(s): February 14, 2002
Received by editor(s) in revised form: August 21, 2002
Published electronically: May 21, 2003
Additional Notes: This work was carried out while the third author was a Dunham Jackson Assistant Professor at the School of Mathematics, University of Minnesota.
The first and third authors were supported in part by the National Science Foundation (Grant DMS-0107609) and by the University of Minnesota Supercomputing Institute
The second author was supported in part by “Deutsche Forschungsgemeinschaft” through SFB 359 and Schwerpunktprogramm ANumE)
Article copyright: © Copyright 2003 American Mathematical Society