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Multigrid methods for nonconforming finite element methods. (English) Zbl 0703.65067

The authors analyze a multigrid algorithm for the Crouzeix-Raviart discretization of the Poisson and Stokes equations in two and three dimensions. In this algorithm the Jacobi relaxation as smoothing procedure and easily computable \(L^ 2\)-projections based on suitable quadrature rules for the transfer from coarse to fine grids and vice versa are used. A detailed convergence analysis of the multigrid algorithm for the Poisson equation is given and the generalization of the convergence analysis to the Stokes equation is outlined.
Reviewer: M.Jung

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35Q30 Navier-Stokes equations
65F10 Iterative numerical methods for linear systems
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