A moving mesh numerical method for hyperbolic conservation laws

Lucier, Bradley J.

doi:10.1090/S0025-5718-1986-0815831-4

A moving mesh numerical method for hyperbolic conservation laws
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Math. Comp. 46 (1986), 59-69 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 $O({N^{ - 1/2}})$.

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