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

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 H and L norms. Reliability and efficiency is 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 non-homogeneous water reservoir concludes the paper.