On Schwarz-type smoothers for saddle point problems. (English) Zbl 1033.65105
The authors analyze the smoothing property of symmetric inexact Uzawa methods as part of a multigrid method for solving symmetric saddle point problems. Additive Schwarz-type iterations are contained as a special case. As an example the theoretical results are applied to the Crouzeix-Raviart mixed finite element method for the Stokes equation. Numerical examples are presented, also for multiplicative Schwarz-type iterations that turn out to perform more efficiently as the additive version.
Reviewer: Rolf Dieter Grigorieff (Berlin)
MSC:
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65F10 | Iterative numerical methods for linear systems |
35J25 | Boundary value problems for second-order elliptic equations |
65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
35Q30 | Navier-Stokes equations |