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 \(\big\| u^\ve(t,\cdot)-u(t,\cdot)\big\|_{{\bf L}^1} %{\strut\L^1}=o(1)\cdot \sqrt{\Delta x} \big|\ln (\Delta x)\big|.\)
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(Accepted September 13, 1996)
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Bressan, A., Marson, A. Error Bounds for a Deterministic Version of the Glimm Scheme. Arch Rational Mech Anal 142, 155–176 (1998). https://doi.org/10.1007/s002050050088
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DOI: https://doi.org/10.1007/s002050050088