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A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations. (English) Zbl 1050.76035
Summary: This paper studies some finite volume discretizations of Darcy’s equations. We propose two finite volume schemes on unstructured meshes and prove their equivalence with either conforming or nonconforming finite element discrete problems. This leads to optimal a priori error estimates. In view of mesh adaptivity, we exhibit residual type error indicators and prove estimates which allow to compare them with the error in a very accurate way.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
65N15 Error bounds for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
Keywords:
mesh adaptivity
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