A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
Ohlberger, Mario
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001), p. 355-387 / Harvested from Numdam
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This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation c t +∇·(𝐮f(c))-∇·(D∇c)+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.

Publié le : 2001-01-01
Classification:  65M15,  35K65,  76M25 
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     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},
     volume = {35},
     year = {2001},
     pages = {355-387},
     mrnumber = {1825703},
     zbl = {0992.65100},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 35 (2001) pp. 355-387. http://gdmltest.u-ga.fr/item/M2AN_2001__35_2_355_0/

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