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Discretisation and multigrid solution of elliptic equations with mixed derivative terms and strongly discontinuous coefficients.(English)Zbl 0818.65113

A new conservative cell centered finite volume method is considered for the accurate solution of elliptic diffusion equations with strongly varying coefficients. Such problems arise in oil reservoir simulation when renormalisation techniques are used to model the reservoir geology. A multigrid scheme based on that ofP. Wesseling [J. Comput. Phys. 79, No. 1, 85-91 (1988;Zbl 0658.65095)] is applied to the resulting algebraic system, showing that a rapid mesh independent convergence rate may be obtained for problems of this type. A series of test problems demonstrates the efficiency of the multigrid procedure in comparison to single grid methods.
Reviewer: L.S.Ioffe (Haifa)

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
76S05 Flows in porous media; filtration; seepage
76M10 Finite element methods applied to problems in fluid mechanics
35J25 Boundary value problems for second-order elliptic equations

Citations:

Zbl 0658.65095

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