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Convergence of relaxation schemes for hyperbolic conservation laws with stiff source terms
Author(s):
A.
Chalabi.
Journal:
Math. Comp.
68
(1999),
955-970.
MSC (1991):
Primary 35L65, 65M05, 65M10
Posted:
February 10, 1999
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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:
10.1090/S0025-5718-99-01089-3
PII:
S 0025-5718(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
Posted:
February 10, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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