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Mixed finite element methods for petroleum reservoir engineering problems. (English) Zbl 0598.76102
Computing methods in applied sciences and engineering VI, Proc. 6th Int. Symp., Versailles 1983, 639-657 (1984).
[For the entire collection see Zbl 0547.00045.]
Mixed finite element methods are considered for computing Darcy velocities for fluid flow problems in a porous medium. It is shown that the five point block-centered finite difference method is a mixed method with special numerical quadratur formulas. Computational results with a block-centered finite difference matrix as a preconditioner for mixed method formulations using the tensor product Raviart-Thomas approximating spaces are presented.

MSC:
76S05 Flows in porous media; filtration; seepage
76M99 Basic methods in fluid mechanics
65N06 Finite difference methods for boundary value problems involving PDEs
Citations:
Zbl 0547.00045