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Vector-Valued Polynomial and Spline Approximation

  • Charles Hall
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)

Abstract

Blended interpolation of vector-valued functions is discussed relative to their applications in the construction of finite elements, mesh generation and table look-up of thermodynamic properties of a gas or liquid. The invertibi1ity of two isoparametric transformations is investigated.

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References

  1. 1.
    J. H. Ahlberg, E. N. Nilson and J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York, 1967.zbMATHGoogle Scholar
  2. 2.
    S. A. Coons, ‘Surfaces for computer-aided design of space forms’, Project MAC, Design Div., Dept. Mech. Engng., Mass. Inst. Tech. (1964). Available from: Clearinghouse for Federal Scientific-Technical Information, National Bureau of Standards, Springfield, Va., U.S.A.Google Scholar
  3. 3.
    P.G. Ciarlet and P. A. Raviart, “interpolation Theory Over Curved Elements with Applications to Finite Element Methods”, Compute. Methods Appl. Mech. Enng. 1, pp. 217–249 (1972).CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    A. E. Frey, C. A. Hall and T. A. Porsching, “Some Results on the Global Inversion of Bilinear and Quadratic Isoparametric Finite Element Transformations”, Math, of Comp. 32 (to appear).Google Scholar
  5. 5.
    A. E. Frey, C. A. Hall and T. A. Porsching, “S0LV8: Inversion by Elimination of the 8-Node Quadratic Isoparametric Mapping”, (submitted).Google Scholar
  6. 6.
    W. J. Gordon, ‘Free-form surface interpolation through curve networks’, Res. Rept. 921, General Motors, Warren, Mich., U.S.A. (1969).Google Scholar
  7. 7.
    W. J. Gordon, ‘Spline-blended surface interpolation through curve networks’, J. Math. Mech., 18, 931–952 (1969).zbMATHMathSciNetGoogle Scholar
  8. 8.
    W. J. Gordon, ‘Blending-function methods for bivariate and multivariate interpolation and approximation’, SIAM J. Numer. Anal. 8, 158–177 (1971).CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    W. J. Gordon and C. A. Hall, “Construction of Curvilinear Co-ordinate Systems and Applications to Mesh Generation”, Int. J. for Numer. Methods in Enng. 7, 461–477 (1973).CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    W. J. Gordon and C. A. Hall, ‘Transfinite element methods: Blending-function interpolation over curved element domains’, Numerishe Mathematik 21, 109–129 (1973).CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    C. A. Hall and B. A. Mutafelija, “Transfinite Interpolation of Steam Tables” J. Computational Physics 18, 79–91 (1975).CrossRefMathSciNetGoogle Scholar
  12. 12.
    P. Morse and H. Feshbach, Methods of Theoretical Physics, Pt. I, McGraw-Hill, New York, 1953.zbMATHGoogle Scholar
  13. 13.
    C. J. de la Vallee Poussin, Cours d’Analyse Infinitesimale, Vol. I, Gauthier-Villars, Paris, 1926.zbMATHGoogle Scholar
  14. 14.
    D. S. Watkins and P. Lancaster, “Some Families of Finite Elements”, J. Inst. Math. Appl. 19, 385–397 (1977).CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    O. C. Zienkiewicz and D. V. Phillips, ‘An automatic mesh generation scheme for plane and curved surfaces by “isoparametric” coordinates’, Int. J. Num. Meth. Engg. 3, 519–528 (1971).CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    O. C. Zienkiewicz, The Finite Element Method in Engineering Science, McGraw-Hill, New York, 1971.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Charles Hall
    • 1
  1. 1.Institute for Computational Mathematics and Applications Department of Mathematics and StatisticsUniversity of PittsburghUSA

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