Error estimates for the convergence of a finite volume discretization of convection-diffusion equations

Jerome Droniou (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We study error estimates for a finite volume discretization of an elliptic equation. We prove that, for $s\\in [0,1]$, if the exact solution belongs to $H^{1+s}$ and the right-hand side is $f+\\div(G)$ with $f\\in L^2$ and $G\\in (H^s)^N$, then the solution of the finite volume scheme converges in discrete $H^1$-norm to the exact solution, with a rate of convergence of order $h^s$ (where $h$ is the size of the mesh).

Mots clés: Convection-diffusion equations; Finite Volume; convergence rate; interpolation

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Jerome Droniou. Error estimates for the convergence of a finite volume discretization of convection-diffusion equations. Journal of Numerical Mathematics, 2003, 11 (1), pp.1-32. ⟨10.1515/156939503322004873⟩. ⟨hal-00018749⟩