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On generalized stationary iterative method for solving the saddle point problems. (English) Zbl 1213.65058

A generalized stationary iterative method is studied for solving saddle point problems. The influence of parameters of the algorithm on the convergence is investigated. Numerical results for a small Stokes problem are presented. They conceal that convergence is not sufficient. Convergence rates that are bounded away from 1 for discretizations on fine meshes are required for the solution of real life problems.

MSC:

65F10 Iterative numerical methods for linear systems
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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