A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems
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- by Vivette Girault, Béatrice Rivière and Mary F. Wheeler;
- Math. Comp. 74 (2005), 53-84
- DOI: https://doi.org/10.1090/S0025-5718-04-01652-7
- Published electronically: March 23, 2004
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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.References
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Bibliographic 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
- 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.
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp. 74 (2005), 53-84
- MSC (2000): Primary 35Q30; Secondary 76D05, 76D07
- DOI: https://doi.org/10.1090/S0025-5718-04-01652-7
- MathSciNet review: 2085402