Cai, Z.; Jones, J. E.; McCormick, S. F.; Russell, T. F. Control-volume mixed finite element methods. (English) Zbl 0941.76050 Comput. Geosci. 1, No. 3-4, 289-315 (1997). 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. Cited in 1 ReviewCited in 51 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage Keywords:local mass conservation; distorted grid; anisotropy; heterogeneity; control-volume mixed finite element method; velocity approximations; block-centered quadrilateral grids; Darcy’s law; second-order convergence PDFBibTeX XMLCite \textit{Z. Cai} et al., Comput. Geosci. 1, No. 3--4, 289--315 (1997; Zbl 0941.76050) Full Text: DOI