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Explicit and Averaging a Posteriori Error Estimates for Adaptive Finite Volume Methods

C. Carstensen, R. Lazarov and S. Tomov
SIAM Journal on Numerical Analysis
Vol. 42, No. 6 (2005), pp. 2496-2521
Stable URL: http://www.jstor.org/stable/4101351
Page Count: 26
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Explicit and Averaging a Posteriori Error Estimates for Adaptive Finite Volume Methods
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Abstract

Local mesh-refining algorithms known from adaptive finite element methods are adopted for locally conservative and monotone finite volume discretizations of boundary value problems for steady-state convection-diffusion-react ion equations. The paper establishes residual-type explicit error estimators and averaging techniques for a posteriori finite volume error control with and without upwind in global H1- and L2-norms. Reliability and efficiency are verified theoretically and confirmed empirically with experimental support for the superiority of the suggested adaptive mesh-refining algorithms over uniform mesh refining. A discussion of adaptive computations in the simulation of contaminant concentration in a nonhomogeneous water reservoir concludes the paper.

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