A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations. (English) Zbl 1050.76035

Achdou, Y.; Bernardi, C.; Coquel, F.

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.

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