Error bounds for the large time step Glimm scheme applied to scalar conservation laws

In this paper we derive an L-1 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(Deltax(1/2)\ log Deltax\) 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.