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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A moving mesh numerical method for hyperbolic conservation laws


Author: Bradley J. Lucier
Journal: Math. Comp. 46 (1986), 59-69
MSC: Primary 65M25; Secondary 35L05
MathSciNet review: 815831
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Abstract: We show that the possibly discontinuous solution of a scalar conservation law in one space dimension may be approximated in $ {L^1}({\mathbf{R}})$ to within $ O({N^{ - 2}})$ by a piecewise linear function with $ O(N)$ nodes; the nodes are moved according to the method of characteristics. We also show that a previous method of Dafermos, which uses piecewise constant approximations, is accurate to $ O({N^{ - 1}})$. These numerical methods for conservation laws are the first to have proven convergence rates of greater than $ O({N^{ - 1/2}})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0815831-4
PII: S 0025-5718(1986)0815831-4
Keywords: Conservation law, adaptive methods, method of characteristics
Article copyright: © Copyright 1986 American Mathematical Society