A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
Institut für Angewandte Mathematik, Universität Freiburg,
Hermann-Herderstr. 10, 79104 Freiburg, Germany. (firstname.lastname@example.org)
Revised: 29 January 2001
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 L1-norm, independent of the diffusion parameter D. 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.
Mathematics Subject Classification: 65M15 / 35K65 / 76M25
Key words: A posteriori error estimates / convection diffusion reaction equation / finite volume schemes / adaptive methods / unstructured grids.
© EDP Sciences, SMAI, 2001