On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
LSEC, Institute of Computational Mathematics,
Academy of Mathematics and System Sciences,
Chinese Academy of Sciences, PO Box 2719, Beijing, 100080,
2 Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan. firstname.lastname@example.org
3 Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada. email@example.com
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
Mathematics Subject Classification: 65F10 / 65N30 / 65N55
Key words: Nonoverlapping domain decomposition / incompressible Navier-Stokes equations / finite elements / nonlinear problems.
© EDP Sciences, SMAI, 2005