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Engineering Analysis with Boundary Elements, Volume 36, Issue 11, November 2012, Pages 1604-1617
Lin-Tian Luh
Department of Mathematics, Providence University, Taiwan
Abstract
This is a continuation of our study about shapeparameter, based on an approach very different from that of Luh. Here we adopt an error bound of convergence order as d→0, where 0<ω<1 is a constant and d denotes essentially the fill-distance. The constant ω is much smaller than the one appears in Luh where the error bound is O(ω1/d) only. Moreover, the constant ω here only mildly depends on the dimension n. It means that for high-dimensional problems the criteria of choosing the shapeparameter presented in this paper are much better than those of Luh. The drawback is that the distribution of data points must be slightly controlled.
