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    Electronic Resource
    Electronic Resource
    Error Bounds for a Deterministic Version of the Glimm Scheme (1998)
    Springer
    Archive for rational mechanics and analysis 142 (1998), S. 155-176 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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 ε be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes $\Delta x$, $\Delta t =O(\Delta x)$ . With a suitable choice of the sampling sequence, we prove the estimate $$\big\| u^\ve(t,\cdot)-u(t,\cdot)\big\|_{{\bf L}^1} %{\strut\L^1}=o(1)\cdot \sqrt{\Delta x} \big|\ln (\Delta x)\big|.$$
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002050050088
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