Osher, Stanley Convergence of generalized MUSCL schemes. (English) Zbl 0627.35061 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 Cited in 3 ReviewsCited in 62 Documents 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 PDF BibTeX XML Cite \textit{S. Osher}, SIAM J. Numer. Anal. 22, 947--961 (1985; Zbl 0627.35061) Full Text: DOI