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

Authors:
C. Carstensen;R. Lazarov;S. Tomov
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2004

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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-reaction 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.