The immersed interface method for nonlinear differential equations with discontinuous coefficients and singular sources

SIAM Journal on Numerical Analysis

Volumn 35, Issue 1, 1998, Pages 177-200

  Wiegmann, Andreas ^a   Bube, Kenneth P ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Discontinuous coefficients; Elliptic equations; Finite difference methods; Immersed interface method; Nonlinear convection terms; Nonlinear implicit methods; Parabolic equations; Traffic flow

Indexed keywords

EID: 0000550068     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003614299529378X     Document Type: Article

References (17)

1. P. E. GILL, W. MURRAY, AND M. H. WRIGHT, Practical Optimization, Academic Press, New York, 1981.
2. R. J. LEVEQUE, Numerical Methods for Conservation Laws, Birkhäuser, Basel. 1992.
3. R. J. LEVEQUE AND Z. LI, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31 (1994), pp 1019-1044.
4. Z. Li, The Immersed Interface Method - A Numerical Approach to Partial Differential Equations with Interfaces, Ph.D. thesis, Department of Applied Mathematics, University of Washington, Seattle, WA, 1994.
5. Z. LI, Immersed interface methods for moving interface problems, Numerical Algorithms, 14 (1997), pp. 269-294.
6. M. H. LIGHTHILL AND G. B. WHITHAM, On kinematic waves, II: A theory of traffic flow on long crowded roads, Proc. Roy. Soc. Lond. Ser. A, 229 (1955), pp. 317-345.
7. P. G. MICHALOPOULOS, P. YI, AND A. S. LYRINTZIS, Continuum modeling of traffic dynamics for congested freeways, Transport. Res. B, 27 (1993), pp. 315-332.
8. G. F. NEWELL, Traffic flow for the morning commute, Transportation Sci., 22 (1988), pp. 47-58.
9. G. F. NEWELL, A simplified theory of kinematic waves in highway traffic, Part I: General theory, Transport. Res. B, 27 (1993), pp. 281-287.
10. G. F. NEWELL, A simplified theory of kinematic waves in highway traffic, Part II: Queueing at freeway bottlenecks, Transport. Res. B, 27 (1993), pp. 289-303.
11. G. F. NEWELL, A simplified theory of kinematic waves in highway traffic, Part III: Multi-destination flows, Transport. Res. B, 27 (1993), pp. 305-313.
12. C. S. PESKIN, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), pp. 220-252.
13. C. S. PESKIN, Lectures on mathematical aspects of physiology, Lectures in Appl. Math., 19 (1981), pp. 69-107.
14. P. I. RICHARDS, Shock waves on the highways, Oper. Res., 4 (1956), pp. 42-51.
15. J. C. STRIKWERDA, Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks/Cole, Pacific Grove, CA, 1989.
16. C. TU AND C. S. PESKIN, Stability and instability in the computation of flows with moving immersed boundaries: A comparison of three methods, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 1361-1376.
17. G. B. WHITHAM, Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974.