@article {1998,
title = {Error bounds for a deterministic version of the Glimm scheme},
journal = {Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176},
number = {SISSA;143/95/M},
year = {1998},
publisher = {Springer},
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 $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$},
doi = {10.1007/s002050050088},
url = {http://hdl.handle.net/1963/1045},
author = {Andrea Marson and Alberto Bressan}
}