Asymptotic-induced numerical methods for conservation laws

Marc Garbey; Jeffrey S. Scroggs

Asymptotic-induced numerical methods for conservation laws

Marc Garbey, Jeffrey S. Scroggs

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.

Original language	English (US)
Title of host publication	Asymptotic Analysis and the Numerical Solution of Partial Differential Equations
Publisher	CRC Press
Pages	75-96
Number of pages	22
ISBN (Electronic)	9781482277067
ISBN (Print)	9780824785383
State	Published - Jan 1 1991

ASJC Scopus subject areas

General Mathematics

Cite this

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abstract = "Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.",

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AB - Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.

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Asymptotic-induced numerical methods for conservation laws

Abstract

ASJC Scopus subject areas

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