Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On a dimensional reduction method. II. Some approximation-theoretic results
HTML articles powered by AMS MathViewer

by M. Vogelius and I. Babuška PDF
Math. Comp. 37 (1981), 47-68 Request permission

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.
References
  • Ivo Babuška, Error-bounds for finite element method, Numer. Math. 16 (1970/71), 322–333. MR 288971, DOI 10.1007/BF02165003
  • I. Babuška, B. A. Szabo, and I. N. Katz, The $p$-version of the finite element method, SIAM J. Numer. Anal. 18 (1981), no. 3, 515–545. MR 615529, DOI 10.1137/0718033
  • M. S. Baouendi and C. Goulaouic, Régularité et théorie spectrale pour une classe d’opérateurs elliptiques dégénérés, Arch. Rational Mech. Anal. 34 (1969), 361–379 (French). MR 249844, DOI 10.1007/BF00281438
    • J. Bergh & J. Löfström, Interpolation Spaces, Springer-Verlag, Berlin and New York, 1976. P. Destuynder, Sur une Justification des Modeles de Plaques et de Coques par les Méthodes Asymptotiques, Doctoral Thesis, Paris VI, January 1980.
  • V. K. Dzyadyk, Vvedenie v teoriyu ravnomernogo priblizheniya funktsiĭ polinomami, Izdat. “Nauka”, Moscow, 1977 (Russian). MR 0612836
    • D. G. Gordeziani, "Accuracy of a variant in the theory of thin shells," Soviet Phys. Dokl., v. 19, 1974, pp. 385-386.
  • J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I, Die Grundlehren der mathematischen Wissenschaften, Band 181, Springer-Verlag, New York-Heidelberg, 1972. Translated from the French by P. Kenneth. MR 0350177
  • G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, New York-Chicago, Ill.-Toronto, Ont., 1966. MR 0213785
    • S. M. Nikol’skiĭ, Approximation of Functions of Several Variables and Imbedding Theorems, Springer-Verlag, Berlin and New York, 1975. F. G. Tricomi, Differential Equations, Blackie & Son, London, 1961. M. Vogelius, A Dimensional Reduction Approach to the Solution of Partial Differential Equations, Ph. D. Thesis, University of Maryland, December 1979.
  • M. Vogelius and I. Babuška, On a dimensional reduction method. I. The optimal selection of basis functions, Math. Comp. 37 (1981), no. 155, 31–46. MR 616358, DOI 10.1090/S0025-5718-1981-0616358-0
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65N99, 65J10
  • Retrieve articles in all journals with MSC: 65N99, 65J10
Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 47-68
  • MSC: Primary 65N99; Secondary 65J10
  • DOI: https://doi.org/10.1090/S0025-5718-1981-0616359-2
  • MathSciNet review: 616359