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An optimal error estimate for upwind Finite Volume methods for nonlinear hyperbolic conservation laws
Authors:Daniel Bouche  Jean-Michel Ghidaglia  Frédéric P Pascal
Institution:aCommissariat à l?Énergie Atomique (CEA DAM), DIF, F-91297 Arpajon, France;bCMLA, ENS Cachan et CNRS, UniverSud, 61 avenue du Président Wilson, F-94235 Cachan, France;cLRC MESO, ENS de Cachan, CEA DAM, 61 avenue du Président Wilson, F-94235 Cachan, France
Abstract:The purpose of this paper is to show that the cell-centered upwind Finite Volume scheme applied to general hyperbolic systems of m conservation laws approximates smooth solutions to the continuous problem at order one in space and time. As it is now well understood, there is a lack of consistency for order one upwind Finite Volume schemes: the truncation error does not tend to zero as the time step and the grid size tend to zero. Here, following our previous papers on scalar equations, we construct a corrector that allows us to prove the expected error estimate for nonlinear systems of equations in one dimension.
Keywords:Finite volume method  Hyperbolic systems of conservation laws  Upwinding  Stability and convergence of numerical methods  Geometric corrector
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