Uniformly high-order accurate nonoscillatory schemes. I. (English) Zbl 0627.65102

Harten, Ami; Osher, Stanley

SIAM J. Numer. Anal. 24, 279-309 (1987).

A new class of second order approximations of nonoscillatory schemes is constructed, in which the solution operator is only required to diminish the number of local extrema in the numerical solution. This properties are achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages.

Reviewer: P.I.Ialamov

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

Keywords:

nonoscillatory shock capturing methods; conservation laws; total variation diminishing schemes; nonoscillatory piecewise-linear reconstruction; cell averages; finite difference scheme; second order approximations; nonoscillatory schemes