On a dimensional reduction method ii some approximation theoretic results

M. Vogelius, I. Babuska

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39 Scopus citations

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 PN, N > 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.

Original languageEnglish (US)
Pages (from-to)47-58
Number of pages12
JournalMathematics of Computation
Volume37
Issue number155
DOIs
StatePublished - Jul 1981
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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