A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations

Ohlberger, Mario

ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 2, pp. 355-387.

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation $c_t+\nabla ·\left(𝐮f\left(c\right)\right)-\nabla ·\left(D\nabla c\right)+\lambda c=0$. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the $L^1$-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.

Classification : 65M15, 35K65, 76M25
Mots clés : a posteriori error estimates, convection diffusion reaction equation, finite volume schemes, adaptive methods, unstructured grids

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