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.

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation c t +·(𝐮f(c))-·(Dc)+λc=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
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     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},
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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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