Convergence of generalized MUSCL schemes. (English) Zbl 0627.35061

Osher, Stanley

SIAM J. Numer. Anal. 22, 947-961 (1985).

Semidiscrete generalizations of the second order extension of Godunov’s scheme, known as the MUSCL (monotonic upstream centered scheme for conservation law) scheme, are constructed, starting with any three point “E” scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

Reviewer: C.A.de Moura

MSC:

35L65	Hyperbolic conservation laws
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

Keywords:

Semidiscrete; Godunov’s scheme; monotonic upstream centered scheme; conservation law; convex; convergent approximation