The convergence rate of approximate solutions for nonlinear scalar conservation laws. (English) Zbl 0765.65092
Let \(\{v^ t(x,t)\}\) be a \(\text{Lip}^ +\)-stable family of approximate solutions for \(u_ t+f(u)_ x=0\) with \(C_ 0^ 1\) initial data. If they are \(\text{Lip}'\)-consistent then they converge to the entropy solution with the rate \({\mathcal O}(\varepsilon)\). \(L^ p\) and pointwise error estimates follow.
Reviewer: J.D.P.Donnelly (Oxford)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
