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Mathematical problems of computational decisions in the finite element method

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Mathematical Aspects of Finite Element Methods

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 606))

Abstract

Present programs for finite element analysis require the user to make numerous, critical, a-priori decisions. They often represent difficult mathematical problems and may influence strongly the accuracy and reliability of the results, the cost of the computation, and other related factors. This paper discusses some of these decisions and their mathematical aspects in the case of several typical examples. More specifically, the questions addressed here concern the effect of different mathematical formulations of the basic problem upon the results, the influence of the desired accuracy on the efficiency of the process, the selection and comparison of different types of elements, and, for nonlinear problems, the choice of efficient methods for solving the resulting finite dimensional equations. In all cases a consistent use of self-adaptive techniques is strongly indicated.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park

    I. Babuška

  2. Computer Science Center and Department of Mathematics, University of Maryland, College Park

    W. C. Rheinboldt

Authors
  1. I. Babuška
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  2. W. C. Rheinboldt
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Editor information

Ilio Galligani Enrico Magenes

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© 1977 Springer-Verlag

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Babuška, I., Rheinboldt, W.C. (1977). Mathematical problems of computational decisions in the finite element method. In: Galligani, I., Magenes, E. (eds) Mathematical Aspects of Finite Element Methods. Lecture Notes in Mathematics, vol 606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064452

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  • DOI: https://doi.org/10.1007/BFb0064452

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08432-7

  • Online ISBN: 978-3-540-37158-8

  • eBook Packages: Springer Book Archive

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