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Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients


Authors: Laurent Gosse and François James
Journal: Math. Comp. 69 (2000), 987-1015
MSC (1991): Primary 65M06, 65M12; Secondary 35F10
DOI: https://doi.org/10.1090/S0025-5718-00-01185-6
Published electronically: March 1, 2000
MathSciNet review: 1670896
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Abstract:

Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equation admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-difference numerical schemes and introduce an appropriate concept of consistency with the continuous problem. Some basic examples including computational results are also supplied.


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Additional Information

Laurent Gosse
Affiliation: Foundation for Research and Technology Hellas, Institute of applied and Computational Mathematics, P.O. Box 1527, 71110 Heraklion, Crete, Greece
Email: laurent@palamida.math.uch.gr

François James
Affiliation: MAPMO, UMR CNRS 6628, Université d’Orléans, BP 6759, 45067 Orléans Cedex 2, France
Email: james@cmapx.polytechnique.fr

DOI: https://doi.org/10.1090/S0025-5718-00-01185-6
Keywords: Linear conservation equations, duality solutions, finite difference schemes, weak consistency, nonconservative product
Received by editor(s): September 9, 1998
Published electronically: March 1, 2000
Additional Notes: Work partially supported by TMR project HCL #ERBFMRXCT960033.
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society