A Moving Mesh Numerical Method
نویسندگان
چکیده
We show that the possibly discontinuous solution of a scalar conservation law in one space dimension may be approximated in i-'(R) to within 0(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 0(N~l). These numerical methods for conservation laws are the first to have proven convergence rates of greater than 0(N~l/2).
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