This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the -norm, independent of the diffusion parameter . The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability of the theoretical results.
Keywords: a posteriori error estimates, convection diffusion reaction equation, finite volume schemes, adaptive methods, unstructured grids
@article{M2AN_2001__35_2_355_0, author = {Ohlberger, Mario}, title = {A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {355--387}, publisher = {EDP-Sciences}, volume = {35}, number = {2}, year = {2001}, mrnumber = {1825703}, zbl = {0992.65100}, language = {en}, url = {http://archive.numdam.org/item/M2AN_2001__35_2_355_0/} }
TY - JOUR AU - Ohlberger, Mario TI - A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 355 EP - 387 VL - 35 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/item/M2AN_2001__35_2_355_0/ LA - en ID - M2AN_2001__35_2_355_0 ER -
%0 Journal Article %A Ohlberger, Mario %T A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 355-387 %V 35 %N 2 %I EDP-Sciences %U http://archive.numdam.org/item/M2AN_2001__35_2_355_0/ %G en %F M2AN_2001__35_2_355_0
Ohlberger, Mario. A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations. ESAIM: Modélisation mathématique et analyse numérique, Volume 35 (2001) no. 2, pp. 355-387. http://archive.numdam.org/item/M2AN_2001__35_2_355_0/
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