NDLI: Error Bounds for Fractional Step Methods for Conservation Laws with Source Terms

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Teng, Zhen-Huan Tang, Tao
Copyright Year	1995
Abstract	Fractional step methods have been used to approximate solutions of scalar conservation laws with source terms. In this paper, the stability and accuracy of the basic fractional step algorithms are analyzed when these algorithms are used to compute discontinuous solutions of nonhomogeneous scalar conservation laws. The authors show that time-splitting methods for conservation laws with source terms always converge to the unique weak solution satisfying the entropy condition. In particular, it is proved that the $L^1 $ errors in the splitting methods are bounded by $O(\sqrt {\Delta t} )$, where $\Delta t$ is the splitting time step. The $L^1 $ convergence rate of a class of fully discrete splitting methods is also investigated.
Starting Page	110
Ending Page	127
Page Count	18
File Format	PDF
ISSN	00361429
DOI	10.1137/0732004
e-ISSN	10957170
Issue Number	1
Volume Number	32
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-14
Access Restriction	Subscribed
Subject Keyword	error estimate Conservation laws hyperbolic conservation laws splitting method monotone scheme Euler method
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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