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Interpolation and Approximation by Piecewise Quadratic C1 — Functions of Two Variables

  • Gerhard Heindl
Part of the ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique book series (ISNM, volume 51)

Summary

This paper presents solutions of some two-dimensional Hermite interpolation problems by C1- interpolants, the restrictions of which to the triangles of a given plane simplicial complex are quadratic polynomials. Approximation properties of the interpolating functions are studied.

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References

  1. 1.
    ALEXANDROFF, P. and HOPF, H.: Topologie. Chelsea Publishing Company, Bronx, New York (1965), (Textually unaltered reprint of the original edition published in Berlin in 1935).Google Scholar
  2. 2.
    CIARLET, P.G. and RAVIART, P.A.: General Lagrange and Hermite Interpolation in ℝn with Applications to Finite Element Methods. Arch. Rational Mech. Anal. 46, 177 – 199 (1972).CrossRefGoogle Scholar
  3. 3.
    HEINDL, G.: Spline — Funktionen mehrerer Veränderlicher. I Definition und Erzeugung durch Integration. Sitz. Ber. Bayer. Akad. Wiss. Math. Nat. Kl. 49–63 (1969).Google Scholar
  4. 4.
    MEINGUET, J.: Structure et estimations de coefficients d’erreurs, R.A.I.R.O. Analyse Numérique, vol. 11, n° 4, 355 – 368, (1977).Google Scholar
  5. 5.
    MEINGUET, J.: A practical method for estimating approximation errors in Sobolev spaces, Institut de Mathematique Pure et Appliquée, Université Catholique de Louvain, Séminaires de Mathématique Appliquée et Mécanique, Rapport n° 104 (1977).Google Scholar
  6. 6.
    POWELL, M.J.D.: Piecewise quadratic surface fitting for contour plotting, in Software for Numerical Analysis, D.J. Evans, ed., Academic Press, 253–272 (1974).Google Scholar
  7. 7.
    ZWART, P.B.: Multivariate splines with nondegenerate partitions, SIAM J. Numer. Anal. 10, 665–673 (1973).CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 1979

Authors and Affiliations

  • Gerhard Heindl

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