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

Published online by Cambridge University Press:  15 April 2002

Mario Ohlberger
Mario Ohlberger*
Affiliation:
Institut für Angewandte Mathematik, Universität Freiburg, Hermann-Herderstr. 10, 79104 Freiburg, Germany. ([email protected])
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Abstract

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation $c_t + \nabla \cdot ( {\bf u}f(c)) - \nabla \cdot (D \nabla c) + \lambda c = 0$ .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.

Keywords

A posteriori error estimatesconvection diffusion reaction equationfinite volume schemesadaptive methodsunstructured grids.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 2 , March 2001 , pp. 355 - 387
Copyright
© EDP Sciences, SMAI, 2001

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