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Mathematics of Computation

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Localization effects and measure source terms in numerical schemes for balance laws

Author: Laurent Gosse
Journal: Math. Comp. 71 (2002), 553-582
MSC (2000): Primary 65M06, 65M12; Secondary 35F25
Published electronically: November 28, 2001
MathSciNet review: 1885615
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Abstract: This paper investigates the behavior of numerical schemes for nonlinear conservation laws with source terms. We concentrate on two significant examples: relaxation approximations and genuinely nonhomogeneous scalar laws. The main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using Riemann-based numerical schemes. Some illustrative and relevant computational results are provided.

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Additional Information

Laurent Gosse
Affiliation: Dipartimento di Matematica Pura e Applicata, Università degli Studi di L’Aquila, Via Vetoio, Località Coppito, 67100 L’Aquila, Italy

Keywords: Balance laws, finite difference schemes, nonconservative products, relaxation schemes
Received by editor(s): December 13, 1999
Published electronically: November 28, 2001
Article copyright: © Copyright 2001 American Mathematical Society