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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Convergence of an Engquist-Osher scheme for a multi-dimensional triangular system of conservation laws


Authors: G. M. Coclite, S. Mishra and N. H. Risebro
Journal: Math. Comp. 79 (2010), 71-94
MSC (2000): Primary 65L06, 35L65; Secondary 76S05
Published electronically: July 10, 2009
MathSciNet review: 2552218
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Abstract: We consider a multi-dimensional triangular system of conservation laws. This system arises as a model of three-phase flow in porous media and includes multi-dimensional conservation laws with discontinuous coefficients as a special case. The system is neither strictly hyperbolic nor symmetric. We propose an Engquist-Osher type scheme for this system and show that the approximate solutions generated by the scheme converge to a weak solution. Numerical examples are also presented.


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Additional Information

G. M. Coclite
Affiliation: Department of Mathematics, University of Bari, via E. Orabona 4, I–70125 Bari, Italy
Email: coclitegm@dm.uniba.it

S. Mishra
Affiliation: Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway
Email: siddharm@math.uio.no

N. H. Risebro
Affiliation: Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway
Email: nilshr@math.uio.no

DOI: http://dx.doi.org/10.1090/S0025-5718-09-02251-0
PII: S 0025-5718(09)02251-0
Received by editor(s): July 30, 2008
Received by editor(s) in revised form: December 13, 2008
Published electronically: July 10, 2009
Additional Notes: The authors thank Kenneth H. Karlsen for many useful discussions. This research is supported in part by the Research Council of Norway. This paper was written as part of the international research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters in Oslo during the academic year 2008–09.
Article copyright: © Copyright 2009 American Mathematical Society