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Mathematics of Computation

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On the convergence of high resolution methods with multiple time scales for hyperbolic conservation laws

Author: Robert Kirby
Journal: Math. Comp. 72 (2003), 1239-1250
MSC (2000): Primary 35L65, 65M12, 65M30
Published electronically: October 29, 2002
MathSciNet review: 1972734
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Abstract: A class of finite volume methods based on standard high resolution schemes, but which allows spatially varying time steps, is described and analyzed. A maximum principle and the TVD property are verified for general advective flux, extending the previous theoretical work on local time stepping methods. Moreover, an entropy condition is verified which, with sufficient limiting, guarantees convergence to the entropy solution for convex flux.

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Additional Information

Robert Kirby
Affiliation: Department of Computer Science, The University of Chicago, 1100 E. 58th St., Chicago, Illinois 60637

Keywords: Spatially varying time steps, upwinding, conservation laws
Received by editor(s): May 10, 2001
Received by editor(s) in revised form: November 30, 2001
Published electronically: October 29, 2002
Additional Notes: Supported by the ASCI/Alliances Center for Astrophysical Thermonuclear Flashes at the University of Chicago under DOE subcontract B341495
Article copyright: © Copyright 2002 American Mathematical Society