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
MathSciNet review: 0375735
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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.
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-  Robert E. Barnhill and Lois Mansfield, Error bounds for smooth interpolation in triangles, J. Approximation Theory 11 (1974), 306–318. MR 0371006
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-  G. M. NIELSON, Private communication, Baltimore, June 1972.
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- 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)
- 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)
- 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)
- 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)
- G. M. NIELSON, Private communication, Baltimore, June 1972.
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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