Geodesic
A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 2, pp. 355-387

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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.

Classification : 65M15, 35K65, 76M25
Keywords: a posteriori error estimates, convection diffusion reaction equation, finite volume schemes, adaptive methods, unstructured grids 
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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 },
     pages = {355--387},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {2},
     year = {2001},
     mrnumber = {1825703},
     zbl = {0992.65100},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_2_355_0/}
}
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Ohlberger, Mario. A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 2, pp. 355-387. http://geodesic.mathdoc.fr/item/M2AN_2001__35_2_355_0/