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March 2005 On Convergence of Semi-discrete High Resolution Schemes with van Leer's Flux Limiter for Conservation Laws
Nan Jiang, Huanan Yang
Methods Appl. Anal. 12(1): 89-102 (March 2005).

Abstract

In the early 1980s, Sweby [19] investigated a class of high resolution schemes using flux limiters for hyperbolic conservation laws. For the convex homogeneous conservation laws, Yang [23] has shown the convergence of the numerical solutions of semi-discrete schemes based on minmod limiter when the general building block of the schemes is an arbitrary $E$-scheme, and based on Chakravarthy-Osher limiter when the building block of the schemes is the Godunov, the Engquist-Osher, or the Lax-Friedrichs to the physically correct solution. Recently, Yang and Jiang [25] have proved the convergence of these schemes for convex conservation laws with a source term. However, the convergence problems of other flux limiter, such as van Leer and superbee have been open. In this paper, we apply the convergence criteria, established in [23] [25] by using Yang's wavewise entropy inequality (WEI) concept, to prove the convergence of the semi-discrete schemes with van Leer's limiter for the aforementioned three building blocks. The result is valid for scalar convex conservation laws in one space dimension with or without a source term. Thus, we have settled one of the aforementioned problems.

Citation

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Nan Jiang. Huanan Yang. "On Convergence of Semi-discrete High Resolution Schemes with van Leer's Flux Limiter for Conservation Laws." Methods Appl. Anal. 12 (1) 89 - 102, March 2005.

Information

Published: March 2005
First available in Project Euclid: 6 June 2006

zbMATH: 1128.65071
MathSciNet: MR2203175

Rights: Copyright © 2005 International Press of Boston

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Vol.12 • No. 1 • March 2005
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