Explicit and averaging a posteriori error estimates for adaptive finite volume methods Academic Article uri icon


  • 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 1- and L 2-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. 2005 Society for Industrial and Applied Mathematics.

published proceedings


author list (cited authors)

  • Carstensen, C., Lazarov, R., & Tomov, S.

citation count

  • 39

complete list of authors

  • Carstensen, C||Lazarov, R||Tomov, S

publication date

  • January 2005