Error bounds for a Deterministic Version of the Glimm Scheme
نویسندگان
چکیده
Consider the hyperbolic system of conservation laws ut + F (u)x = 0. Let u be the unique viscosity solution with initial condition u(0, x) = ū(x), and let u be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes ∆x, ∆t = O(∆x). With a suitable choice of the sampling sequence, we prove the estimate ∥∥uG(t, ·)− u(t, ·)∥∥ L1 = o(1) · √ ∆x ∣∣ ln(∆x)∣∣.
منابع مشابه
Error bounds for a Deterministic
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) = u(x), and let u " be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes x, t = O((x). With a suitable choice of the sampling sequence, we prove the estimate u " (t;) ? u(t;) L 1 = o(1) p x ln((x) :
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