A posteriori error estimates for finite volume element approximations of convection-diffusion-reaction equations
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abstract
We present the results of a study on a posteriori error control strategies for finite volume element approximations of second order elliptic differential equations. Finite volume methods ensure local mass conservation and, combined with some up-wind strategies, give monotone solutions. We adapt the local refinement techniques known from the finite element method to the finite volume discretizations of various boundary value problems for steady-state convection-diffusion-reaction equations. In this paper we derive and study a residual type error estimator and illustrate its practical performance on a series of computational tests in 2 and 3 dimensions. Our tests show that the discussed locally conservative approximation methods with a posteriori error control can be used successfully in numerical simulation of fluid flow and transport in porous media. 2002 Kluwer Academic Publishers.
