Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4640108 | Journal of Computational and Applied Mathematics | 2011 | 17 Pages |
In this paper we estimate the error of upwind first order finite volume schemes applied to scalar conservation laws. As a first step, we consider standard upwind and flux finite volume scheme discretization of a linear equation with space variable coefficients in conservation form. We prove that, in spite of their lack of consistency, both schemes lead to a first order error estimate. As a final step, we prove a similar estimate for the nonlinear case. Our proofs rely on the notion of geometric corrector, introduced in our previous paper by Bouche et al. (2005) [24] in the context of constant coefficient linear advection equations.
► Convergence errors of upwind finite volume methods in one dimension are estimated. ► Linear convection and nonlinear scalar problems are considered. ► A linear standard upwind method and a flux finite volume method are compared. ► Geometric corrector and finite differences analyses are used to prove the estimate. ► The geometric corrector depends only on the mesh and datas of the problem.