A Method of Fractional Steps for Scalar Conservation Laws without the CFL Condition

Helge Holden, Nils Henrik Risebro

Type: Article

Publication Date: 1993-01-01

Citations: 0

DOI: https://doi.org/10.2307/2153162

Abstract

We present a numerical method for the «-dimensional initial value problem for the scalar conservation law u{xx , ... , x" , t)¡ + Y!¡=\ fi(uOur method is based on the use of dimensional splitting and Dafermos's method to solve the one-dimensional equations.This method is unconditionally stable in the sense that the time step is not limited by the space discretization.Furthermore, we show that this method produces a subsequence which converges to the weak entropy solution as both the time and space discretization go to zero.Finally, two numerical examples are discussed.

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Works That Cite This (0)

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Works Cited by This (5)

Action	Title	Year	Authors
+	FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES	1970	S N Kružkov
+	Weak solution of the Cauchy problem for a multi-dimensional quasi-linear equation	1967	Nikolai Kuznetsov
+	A numerical method for first order nonlinear scalar conservation laws in one-dimension	1988	Helge Holden Lars Holden Raphaël Høegh-Krohn
+	Polygonal approximations of solutions of the initial value problem for a conservation law	1972	Constantine M. Dafermos
+	Global solutions of the cauchy problem for quasi‐linear first‐order equations in several space variables	1966	Edward D. Conway Joel Smoller