Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable

Abstract

We consider Darcy's equations with variable permeability coefficient in a two- or three-dimensional domain. We propose a finite volume scheme, which turns out to be equivalent to a finite element problem, and we derive optimal a priori error estimates. We describe error indicators and prove that they provide an appropriate tool for mesh adaptivity, since estimates allow to compare them with the error.