### Error bounds for a Deterministic Version of the Glimm Scheme

A. Bressan and A. Marson

Abstract: Consider the hyperbolic system of conservation laws $u_t F(u)_x=0. Let$u$be the unique viscosity solution with initial condition$u(0,x)=\bar u(x)$and let$u^\varepsilon$be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes$\Delta x,\Delta t=O(\Delta x). With a suitable choise of the sampling sequence, we prove the estimate $$\left\Vert u^\varepsilon(t,\cdot)-u(t,\cdot) \right\Vert_1=o(1)\cdot\sqrt{\Delta x}\vert\ln\Delta x\vert.$$

Paper:
Available as PostScript
Title:
Error bounds for a Deterministic Version of the Glimm Scheme
Author(s):
A. Bressan, <bressan@sissa.it>
A. Marson, <marson@bsing.ing.unibs.it>
Submitted by:
<marson@bsing.ing.unibs.it> September 6 1996.

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