An optimal error estimate for upwind Finite Volume methods for nonlinear hyperbolic conservation laws

• Autores: Daniel Bouche, Jean-Michel Ghidaglia, Frédéric P. Pascal
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 61, Nº. 11, 2011, págs. 1114-1131
• Idioma: inglés
• DOI: 10.1016/j.apnum.2011.07.005
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• Resumen

  • 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.