A moving mesh numerical method for hyperbolic conservation laws
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 by Bradley J. Lucier PDF
 Math. Comp. 46 (1986), 5969 Request permission
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 $O({N^{  1/2}})$.References

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Additional Information
 © Copyright 1986 American Mathematical Society
 Journal: Math. Comp. 46 (1986), 5969
 MSC: Primary 65M25; Secondary 35L05
 DOI: https://doi.org/10.1090/S00255718198608158314
 MathSciNet review: 815831