## 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

### Keywords:

mixed finite element formulation; Poisson equation
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### References:

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