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Error analysis of piecewise constant pressure approximations of Darcy’s law. (English) Zbl 1116.76051

Summary: We present a short discussion on some finite element formulations for linear elliptic problems. For the sake of simplicity, we consider Poisson equation \(- \Delta p = f\), taking the notation from Darcy’s law. Among the zillions of such methods, we concentrate our attention on FEM leading to a final system of linear algebraic equations \(MP = F\), where each unknown \(P_{i}\) represents the constant value of the approximated pressure \(p_{h}\) in a single element. It is indeed well-known that for some applications there is a certain demand for these types of schemes.

MSC:

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