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 | References | Similar Articles | Additional Information

Abstract: Boolean sum interpolation theory is used to derive a polynomial interpolant which interpolates a function , and its derivatives of order *N* and less, on the boundary of a triangle *T*. A triangle with one curved side is also considered.

**[1]**R. E. BARNHILL, G. BIRKHOFF & W. J. GORDON, "Smooth interpolation in triangles,"*J. Approximation Theory*, v. 8, 1973, pp. 114-128. MR**0368382 (51:4623)****[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