A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 2, p. 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
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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {35},
number = {2},
year = {2001},
pages = {355-387},
zbl = {0992.65100},
mrnumber = {1825703},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_2_355_0}
}

Ohlberger, Mario. A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 2, pp. 355-387. http://www.numdam.org/item/M2AN_2001__35_2_355_0/

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