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.
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Lazarov, R., Tomov, S. A Posteriori Error Estimates for Finite Volume Element Approximations of Convection–Diffusion–Reaction Equations. Computational Geosciences 6, 483–503 (2002). https://doi.org/10.1023/A:1021247300362
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DOI: https://doi.org/10.1023/A:1021247300362