Error estimate for the upwind finite volume method for the nonlinear scalar conservation law
The error of upwind first order finite volume schemes is estimated and applied to scalar conservation laws. As the first step, the authors consider standard upwind and flux finite volume scheme discretization of a linear equation with space variable coefficients in conservation form. It is proven that, in spite of their lack of consistency, both schemes lead to a first order error estimate. As a final step, a similar estimate for the nonlinear case is proven. The proofs rely on the notion of geometric corrector introduced in a previous paper by the authors [SIAM J. Numer. Anal. 43, No.~2, 578--603 (2005; Zbl 1094.65089)] in the context of constant coefficient linear advection equations.
scientific article; zbMATH DE number 5955996
scientific article