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.


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