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Polynomial interpolation to boundary data on triangles


Authors: R. E. Barnhill and J. A. Gregory
Journal: Math. Comp. 29 (1975), 726-735
MSC: Primary 65D10
DOI: https://doi.org/10.1090/S0025-5718-1975-0375735-3
MathSciNet review: 0375735
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Abstract: Boolean sum interpolation theory is used to derive a polynomial interpolant which interpolates a function $ F \in {C^N}(\bar T)$, and its derivatives of order N and less, on the boundary $ \partial T$ of a triangle T. A triangle with one curved side is also considered.


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

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  • [2] R. E. BARNHILL & L. MANSFIELD, "Error bounds for smooth interpolation in triangles," J. Approximation Theory, v. 11, 1974, pp. 306-318. MR 0371006 (51:7229)
  • [3] G. BIRKHOFF, "Tricubic polynomial interpolation," Proc. Nat. Acad. Sci. U.S.A, v. 68, 1971, pp. 1162-1164. MR 45 #9030. MR 0299982 (45:9030)
  • [4] W. J. GORDON & J. A. WIXOM, "Pseudo-harmonic interpolation on convex domains," SIAM J. Numer. Anal., v. 11, 1974, pp. 909-933. MR 0368384 (51:4625)
  • [5] J. A. MARSHALL & A. R. MITCHELL, "An exact boundary technique for improved accuracy in the finite element method," J. Inst. Math. Appl., v. 12, 1973, pp. 355-362. MR 0329287 (48:7629)
  • [6] G. M. NIELSON, Private communication, Baltimore, June 1972.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0375735-3
Keywords: Bivariate interpolation, Coons patches for triangles, polynomial blending functions, blending function interpolation methods, Boolean sum interpolation, curved boundary finite elements
Article copyright: © Copyright 1975 American Mathematical Society

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