Preprint 1996-032

Error bounds for a Deterministic Version of the Glimm Scheme

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, mailto:bressan@sissa.it

A. Marson, mailto:marson@bsing.ing.unibs.it

Submitted by:

mailto:marson@bsing.ing.unibs.it September 6 1996.