Preprint 2002-028

A Posteriori Error Estimate for Front-Tracking for Nonlinear Systems of Conservation Laws

Marc Laforest

Abstract: We demonstrate an a posteriori error estimate in the $L^1$ norm for front-tracking approximate solutions to hyperbolic systems of nonlinear conservation laws. Extending the $L^1$-stability result of Bressan, Liu, and Yang we use their $L^1$-equivalent functional for pairs of front-tracking approximations and identify the leading order contribution to the numerical error. This leading term is closely related to the residual of the approximation and determines an a posteriori bound of the error. We demonstrate the estimate for the front-tracking approximations of Risebro, which are extensions to systems of Dafermos' polygonal approximations.

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Marc Laforest, <>
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<> May 15 2002.

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