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

Authors:
Robert Kirby
Affiliations:
Department of Computer Science, The University of Chicago, 1100 E. 58th St., Chicago, Illinois
Venue:
Mathematics of Computation
Year:
2003

Citing 2
Cited 3

Adaptive local refinement with octree load balancing for the parallel solution of three-dimensional conservation laws

Journal of Parallel and Distributed Computing - Special issue on dynamic load balancing
High Resolution Schemes for Conservation Laws with Locally Varying Time Steps

SIAM Journal on Scientific Computing

Self-adaptive time integration of flux-conservative equations with sources

Journal of Computational Physics
Compact integration factor methods for complex domains and adaptive mesh refinement

Journal of Computational Physics
Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales

Journal of Scientific Computing

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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.