Convergence of relaxation schemes

for hyperbolic conservation laws

with stiff source terms

Author:
A. Chalabi

Journal:
Math. Comp. **68** (1999), 955-970

MSC (1991):
Primary 35L65, 65M05, 65M10

DOI:
https://doi.org/10.1090/S0025-5718-99-01089-3

Published electronically:
February 10, 1999

MathSciNet review:
1648367

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We focus in this study on the convergence of a class of relaxation numerical schemes for hyperbolic scalar conservation laws including stiff source terms. Following Jin and Xin, we use as approximation of the scalar conservation law, a semi-linear hyperbolic system with a second stiff source term. This allows us to avoid the use of a Riemann solver in the construction of the numerical schemes. The convergence of the approximate solution toward a weak solution is established in the cases of first and second order accurate MUSCL relaxed methods.

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Additional Information

**A. Chalabi**

Affiliation:
CNRS, Umr Mip 5640 - UFR Mig Universite P. Sabatier, Route de Narbonne 31062 Toulouse cedex France

Email:
chalabi@mip.ups-tlse.fr

DOI:
https://doi.org/10.1090/S0025-5718-99-01089-3

Keywords:
Conservation laws,
stiff source term,
relaxation scheme,
fully implicit scheme,
semi-implicit scheme,
TVD scheme,
MUSCL method,
entropy solution

Received by editor(s):
April 29, 1997

Received by editor(s) in revised form:
October 14, 1997

Published electronically:
February 10, 1999

Article copyright:
© Copyright 1999
American Mathematical Society