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A Comparison of Three Solvers for the Incompressible Navier--Stokes Equations

by John V., Matthies G., Mitkova T.I., Tobiska L., Vassilevski P.S..

Series: 1999-13, Preprints

65N22 Solution of discretized equations
65N55 Multigrid methods; domain decomposition

Three solvers
for saddle point problems arising from the linearization
and discretization of the steady state incompressible
Navier--Stokes equations are numerically studied.
The numerical tests are based on
nonconforming finite element
approximations of lowest order in two--dimensional domains
using isotropic meshes. The investigated
solvers are coupled multigrid methods with Vanka--type smoothers,
flexible GMRES with a block--diagonal preconditioner proposed by Vassilevski
and Lazarov (1996), and flexible GMRES with a coupled preconditioner which is
based on an algebraic multigrid method.

incompressible Navier-Stokes equations, coupled multigrid methods, preconditioned flexible GMRES, algebraic multigrid methods

This paper was published in:
Large-Scle Scientific Computations of Engineering and Environmental Problems II, ed. by M. Griebel et al., Notes on Numerical Fluid Mechanics. v. 73, 215 - 222, Vieweg-Verlag, 2000