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

Girault, Vivette; Rivière, Béatrice; Wheeler, Mary

doi:10.1090/S0025-5718-04-01652-7

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 PDF

Math. Comp. 74 (2005), 53-84 Request permission

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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