Convergence of relaxation schemes for hyperbolic conservation laws with stiff source terms

@article{Chalabi1999ConvergenceOR,
  title={Convergence of relaxation schemes for hyperbolic conservation laws with stiff source terms},
  author={Abdallah Chalabi},
  journal={Math. Comput.},
  year={1999},
  volume={68},
  pages={955-970}
}
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… CONTINUE READING
Highly Influential
This paper has highly influenced 10 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 108 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 36 extracted citations

Convergence Rates for Relaxation Schemes Approximating Conservation Laws

SIAM J. Numerical Analysis • 2000
View 7 Excerpts
Highly Influenced

The LIP+ -Stability and Error Estimates for a Relaxation Scheme

SIAM J. Numerical Analysis • 2000
View 4 Excerpts
Method Support
Highly Influenced

108 Citations

051015'98'03'09'15
Citations per Year
Semantic Scholar estimates that this publication has 108 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 28 references

Kruzkov, First order quasi-linear equations in several independent variables

S N.
Math. USSR-Sb., • 1970
View 4 Excerpts
Highly Influenced

Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms

S. Jin
J. Comput. Phys., • 1995
View 4 Excerpts
Highly Influenced

Hyperbolic conservation laws with source terms: Errors of the shock location

P. Klingenstein
PhD thesis, Suiss Federal Institute of Tecnology, • 1997
View 2 Excerpts

Hyperbolic conservation laws with stiff relaxation terms and entropy

C. D. Levermore, T. P. Liu
Comm . Pure Appl . Math . • 1997

An error bound for the polygonal approximation of conservation laws with source

A. Chalabi
terms, Comput. & Math. Appl., • 1996
View 1 Excerpt

Convergence of relaxation schemes for conservation

D. Aregba-Driollet, R. Natalini
laws, Appl. Anal • 1996