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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On a dimensional reduction method. II. Some approximation-theoretic results
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by M. Vogelius and I. Babuška PDF
Math. Comp. 37 (1981), 47-68 Request permission


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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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 47-68
  • MSC: Primary 65N99; Secondary 65J10
  • DOI:
  • MathSciNet review: 616359