Convergence of an Engquist-Osher scheme for a multi-dimensional triangular system of conservation laws
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- by G. M. Coclite, S. Mishra and N. H. Risebro PDF
- Math. Comp. 79 (2010), 71-94 Request permission
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.References
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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
- 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.
- © Copyright 2009 American Mathematical Society
- Journal: Math. Comp. 79 (2010), 71-94
- MSC (2000): Primary 65L06, 35L65; Secondary 76S05
- DOI: https://doi.org/10.1090/S0025-5718-09-02251-0
- MathSciNet review: 2552218