00924nas a2200121   4500008004100000245006500041210006500106260001300171520054200184100001900726700002100745856003600766       1998                        en  d00aError bounds for a deterministic version of the Glimm scheme0 aError bounds for a deterministic version of the Glimm scheme  bSpringer3 aConsider 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 $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$1 aMarson, Andrea1 aBressan, Alberto  uhttp://hdl.handle.net/1963/1045