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 uε be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes Δx, Δt = O(Δx). With a suitable choice of the sampling sequence, we prove the estimate ∥uε(t, ·) - u(t, ·)∥L = o(1) · √Δx|ln(Δx)|.
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering