A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations
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- Achdou, Y., Bernardi, C. & Coquel, F. Numer. Math. (2003) 96: 17. doi:10.1007/s00211-002-0436-7
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This paper is devoted to the numerical analysis of 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.