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On a dimensional reduction method. II. Some approximation-theoretic results

Authors: M. Vogelius and I. Babuška
Journal: Math. Comp. 37 (1981), 47-68
MSC: Primary 65N99; Secondary 65J10
MathSciNet review: 616359
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Abstract: This paper is the second in a series of three that analyze a method of dimensional reduction. It contains some results for approximation of functions on the interval $[ - 1,1]$ with elements from the null-space of ${P^N}$, $N \geqslant 1$, where P is a second-order ordinary differential operator. A special case of this is approximation by polynomials. The one-dimensional results are used as a tool to prove similar versions in several dimensions. These multi-dimensional results are directly related to the approximate method of dimensional reduction that was introduced in [13], and they lead to statements about the convergence properties of this approach. The third paper, which analyzes the adaptive aspects of the method, is forthcoming.

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Article copyright: © Copyright 1981 American Mathematical Society