John, V.; Tobiska, L. A coupled multigrid method for nonconforming finite element discretizations of the 2D-Stokes equation. (English) Zbl 0963.65126 Computing 64, No. 4, 307-321 (2000). 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. Reviewer: Pavel Burda (Praha) Cited in 1 ReviewCited in 4 Documents 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 Keywords:Braess-Sarazin smoother; numerical examples; multigrid method; Stokes equation; nonconforming finite elements; convergence Citations:Zbl 0874.65095 PDFBibTeX XMLCite \textit{V. John} and \textit{L. Tobiska}, Computing 64, No. 4, 307--321 (2000; Zbl 0963.65126) Full Text: DOI