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Control-volume mixed finite element methods. (English) Zbl 0941.76050

From the summary: We present a control-volume mixed finite element method that provides procedure for obtaining velocity approximations on irregular (i.e., distorted logically rectangular) block-centered quadrilateral grids. The control-volume formulation of Darcy’s law can be viewed as a discretization into element-sized “tanks” with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block-by-block conservation in the usual mixed discretization of the mass-conservation equation. Numerical results in two dimensions show second-order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
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