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Non-nested multi-level solvers for finite element discretisations of mixed problems. (English) Zbl 1006.65137
This paper deals with multi-level solvers for finite element discretizations of mixed problems which allow different discretizations, in particular the use of different finite element spaces on each level of the multi-grid hierarchy. The crucial point in the construction of such multi-level methods is the transfer operator between the finite element spaces defined on different levels.
The authors show that rather simple \(L^2\)-stable prolongations guarantee already the convergence of the two-level method for a sufficiently large number of smoothing steps with a Braess-Sarazin type smoother. As a concrete application Stokes and Navier-Stokes equations are solved.

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35Q30 Navier-Stokes equations
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