%0 Journal Article %J Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176 %D 1998 %T Error bounds for a deterministic version of the Glimm scheme %A Andrea Marson %A Alberto Bressan %X 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 $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$ %B Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176 %I Springer %G en %U http://hdl.handle.net/1963/1045 %1 2811 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:05Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1007/s002050050088