Multigrid preconditioned conjugate-gradient solver for mixed finite-element method. (English) Zbl 1198.65064

The mixed finite-element approximation of a porous media flow by the lowest order Raviart-Thomas elements is transformed by elimination of the fluxes into a positive definite Schur complement system for the pressures, which is solved by conjugate gradients preconditioned by a multigrid method for related cell-centered finite differences. The matrix of the fluxes can be inverted cheaply for rectangular grids, but for distorted meshes, the elimination is done by inner iterations with incomplete Cholesky preconditioning.


65F10 Iterative numerical methods for linear systems
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
65N06 Finite difference methods for boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
76M10 Finite element methods applied to problems in fluid mechanics
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