Mathematics of Computation

Author(s): Bernardo Cockburn; Guido Kanschat; Dominik Schötzau.
Journal: Math. Comp. 73 (2004), 569-593.
MSC (2000): Primary 65N30
Posted: May 21, 2003
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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

- 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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Bernardo Cockburn
Affiliation: School of Mathematics, University of Minnesota, Vincent Hall, Minneapolis, Minnesota 55455
Email: cockburn@math.umn.edu

Guido Kanschat
Affiliation: Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293/294, 69120 Heidelberg, Germany
Email: kanschat@dgfem.org

Dominik Schötzau
Affiliation: Department of Mathematics, University of Basel, Rheinsprung~21, 4051 Basel, Switzerland
Email: schotzau@math.unibas.ch

DOI: 10.1090/S0025-5718-03-01552-7
PII: S 0025-5718(03)01552-7
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
Posted: 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)
Copyright of article: Copyright 2003, American Mathematical Society

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