An error estimate for a finite volume scheme for a diffusion–convection problem on a triangular mesh

Abstract

Abstract We study here a finite volume scheme for a diffusion‐convection equation on an open bounded set Ω of ℝ 2 , using a triangular mesh for the discretization of Ω. The 4‐point numerical scheme is presented along with the geometrical assumptions on the mesh. An error estimate of order h on the discrete L 2 norm is obtained, where h denotes the “size” of the mesh. The proof uses an estimate of order h of the consistency error on the fluxes and an estimate of the number of edges of the mesh between one given triangle and the boundary Ω. © 1995 John Wiley & Sons, Inc.