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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

Béatrice Rivière
Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray, Pittsburgh, Pennsylvania 15260

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

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