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A coupled multigrid method for nonconforming finite element discretizations of the 2D-Stokes equation. (English) Zbl 0963.65126

Authors’ abstract: The paper investigates a multigrid method for the solution of the saddle point formulation of the discrete Stokes equation obtained with inf-sub stable nonconforming finite elements of lowest order. A smoother proposed by D. Braess and R. Sarazin [Appl. Numer. Math. 23, No. 1, 3-19 (1997; Zbl 0874.65095)] is used and \({\mathcal L}^2\)-projection as well as simple averaging are considered as prolongation. The \(W\)-cycle convergence in the \({\mathcal L}^2\)-norm of the velocity with a rate independently of the level and linearly decreasing with increasing number of smoothing steps is proven. Numerical tests confirm the theoretically predicted results.

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
35Q30 Navier-Stokes equations
65F10 Iterative numerical methods for linear systems

Citations:

Zbl 0874.65095
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