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A stabilized mixed finite element method for Darcy flow. (English) Zbl 1015.76047
Summary: We develop new stabilized mixed finite element methods for Darcy flow. Stability and an a priori error estimate in the “stability norm” are established. A wide variety of convergent finite elements present themselves, unlike the classical Galerkin formulation which requires highly specialized elements. An interesting feature of the formulation is that there are no mesh-dependent parameters. Numerical tests confirm the theoretical results.

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