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

DOI:
https://doi.org/10.1090/S0025-5718-1986-0815831-4

MathSciNet review:
815831

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the possibly discontinuous solution of a scalar conservation law in one space dimension may be approximated in to within by a piecewise linear function with 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 . These numerical methods for conservation laws are the first to have proven convergence rates of greater than .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0815831-4

Keywords:
Conservation law,
adaptive methods,
method of characteristics

Article copyright:
© Copyright 1986
American Mathematical Society