Kruzkov’s estimates for scalar conservation laws revisited. (English) Zbl 0955.65069
Summary: We give a synthetic statement of Kruzhkov-type estimates for multidimensional scalar conservation laws [cf. S. N. Kruzhkov, Mat. Sb., N. Ser. 81(123), 228-255 (1970; Zbl 0202.11203)]. We apply it to obtain various estimates for different approximation problems. In particular, we recover for a model equation the rate of convergence in \(h^{1/4}\) known for finite volume methods on unstructured grids.
MSC:
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 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 |
| 35L65 | Hyperbolic conservation laws |
