Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4645596 | Applied Numerical Mathematics | 2011 | 18 Pages |
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.
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