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An algorithm for determining invertible quadratic isoparametric finite element transformations


Author: David A. Field
Journal: Math. Comp. 37 (1981), 347-360
MSC: Primary 65N30; Secondary 65H10
DOI: https://doi.org/10.1090/S0025-5718-1981-0628700-5
MathSciNet review: 628700
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Abstract: This paper derives an algorithm which determines the invertibility of arbitrary two-dimensional quadratic isoparametric finite element transformations. Theorems verifying the algorithm and guiding the construction of invertible transformations are proven.


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

  • [1] A. E. Frey, C. A. Hall & T. A. Porsching, "Some results on the global inversion of bilinear and quadratic isoparametric finite element transformations," Math. Comp., v. 32, 1978, pp. 725-749. MR 0474877 (57:14508)
  • [2] W. Fulks, Advanced Calculus, Wiley, New York, 1961. MR 0122922 (23:A254)
  • [3] A. S. Householder, "Bigradients and the problem of Routh and Hurwitz," SIAM Rev., v. 10, 1968, pp. 56-66. MR 0229805 (37:5371)
  • [4] C. J. de la Vallée Poussin, Cours d'Analyse Infinitésimale, Vol. I, 7th ed., Louvain, 1930.
  • [5] B. L. Van Der Waerden, Modern Algebra, Vol. II, Ungar, New York, 1950.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1981-0628700-5
Article copyright: © Copyright 1981 American Mathematical Society

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