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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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Keywords: Conservation law, adaptive methods, method of characteristics
Article copyright: © Copyright 1986 American Mathematical Society