×

zbMATH — the first resource for mathematics

The discrete one-sided Lipschitz condition for convex scalar conversation laws. (English) Zbl 0637.65090
The one-sided Lipschitz condition (OSLC), enforcing both the entropy condition and total variation boundedness for physical solutions to convex scalar conservation laws is considered. The definition of OSLC (and weakly OSLC) consistent schemes is given, and this consistency is proved for certain first order accurate schemes. The convergence of OSLC consistent scheme for the periodic initial boundary value problem is also proved. The authors introduce a new fully second order OSLC consistent MUSCL scheme, describe an OSLC consistent method of lines and consider the properties of the modified equation. Some numerical results are discussed and some open problems are posed.
Reviewer: V.Kamen

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
PDF BibTeX Cite
Full Text: DOI