Preprint 2001-024

Error Bounds for the Large Time Step Glimm Scheme Applied to Scalar Conservation Laws

J. Huang, J. Wang, and G. Warnecke

Abstract: In this paper we derive an L1 error bound for the large time step, i.e. large Courant number, version of the Glimm scheme when used for the approximation of solutions to a genuinely nonlinear, i.e. convex, scalar conservation law for a generic class of piecewise constant data. We show that the error is bounded by O(\Delta x1/2|log \Delta x|) for Courant numbers up to 1. The order of the error is the same as that given by Hoff and Smoller [5] in 1985 for the Glimm scheme under the restriction of Courant numbers up to 1/2.

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J. Huang
J. Wang, <>
G. Warnecke, <>
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<> July 10 2001.

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