Achdou, Y.; Bernardi, C.; Coquel, F. A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations. (English) Zbl 1050.76035 Numer. Math. 96, No. 1, 17-42 (2003). 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. Cited in 44 Documents 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 PDF BibTeX XML Cite \textit{Y. Achdou} et al., Numer. Math. 96, No. 1, 17--42 (2003; Zbl 1050.76035) Full Text: DOI