On the convergence of high resolution methods with multiple time scales for hyperbolic conservation laws
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- Math. Comp. 72 (2003), 1239-1250 Request permission
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.References
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Additional Information
- Robert Kirby
- Affiliation: Department of Computer Science, The University of Chicago, 1100 E. 58th St., Chicago, Illinois 60637
- Email: kirby@cs.uchicago.edu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 1239-1250
- MSC (2000): Primary 35L65, 65M12, 65M30
- DOI: https://doi.org/10.1090/S0025-5718-02-01469-2
- MathSciNet review: 1972734