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On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach


Authors: M. Vogelius and I. Babuška
Journal: Math. Comp. 37 (1981), 361-384
MSC: Primary 65N99; Secondary 65J10
DOI: https://doi.org/10.1090/S0025-5718-1981-0628701-7
MathSciNet review: 628701
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Abstract: This paper is the last in a series of three which analyze an adaptive approximate approach for solving $ (n + 1)$-dimensional boundary value problems by replacing them with systems of equations in n-dimensional space.

In this paper we show how to find reliable a posteriori estimates for the error and how these can also be used in the design of an adaptive strategy. Various numerical examples are contained in the paper.


References [Enhancements On Off] (What's this?)

  • [1] I. Babuška & W. C. Rheinboldt, "Reliable error estimation and mesh adaptation for the finite element method," Computational Methods in Nonlinear Mechanics (J. T. Oden, Ed.), North-Holland, Amsterdam, 1980, pp. 67-108. MR 576902 (82f:65109)
  • [2] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Groningen, 1976. MR 0390843 (52:11666)
  • [3] V. Dunder & S. Ridlon, "Practical applications of the finite element method," ASCE J. Structures Division ST1, January 1978, pp. 9-21.
  • [4] N. Dunford & J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.
  • [5] M. Vogelius, Ph.D. Thesis, University of Maryland, December 1979.
  • [6] M. Vogelius & I. Babuška, "On a dimensional reduction method. I. The optimal selection of basis functions," Math. Comp., v. 37, 1981, pp. 31-46. MR 616358 (83c:65259a)
  • [7] M. Vogelius & I. Babuška, "On a dimensional reduction methood. II. Some approximation-theoretic results," Math. Comp., v. 37, 1981, pp. 47-68. MR 616359 (83c:65259b)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1981-0628701-7
Article copyright: © Copyright 1981 American Mathematical Society

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