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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems


Authors: Vivette Girault, Béatrice Rivière and Mary F. Wheeler
Journal: Math. Comp. 74 (2005), 53-84
MSC (2000): Primary 35Q30; Secondary 76D05, 76D07
Published electronically: March 23, 2004
MathSciNet review: 2085402
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Abstract: A family of discontinuous Galerkin finite element methods is formulated and analyzed for Stokes and Navier-Stokes problems. An inf-sup condition is established as well as optimal energy estimates for the velocity and $L^2$ estimates for the pressure. In addition, it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces.


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Additional Information

Vivette Girault
Affiliation: Université Pierre et Marie Curie, Paris VI, Laboratoire Jacques-Louis Lions, $4$, place Jussieu, F-75230 Paris Cedex 05, France
Email: girault@ann.jussieu.fr

Béatrice Rivière
Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray, Pittsburgh, Pennsylvania 15260
Email: riviere@math.pitt.edu

Mary F. Wheeler
Affiliation: The Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The University of Texas, 201 E. 24th St., Austin, Texas 78712
Email: mfw@ices.utexas.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-04-01652-7
PII: S 0025-5718(04)01652-7
Keywords: Discontinuous finite element methods, Navier-Stokes, domain decomposition, nonconforming grids, local mass conservation
Received by editor(s): March 26, 2002
Received by editor(s) in revised form: May 9, 2003
Published electronically: March 23, 2004
Additional Notes: Each author was supported in part by DOD Pet2 Grant and NSF Grants KDI#DMS-9873326 and ITR#EIA-0121523.
Article copyright: © Copyright 2004 American Mathematical Society