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Mansfield, Lois

Interpolation to boundary data in tetrahedra with applications to compatible finite elements. (English) Zbl 0361.41002

J. Math. Anal. Appl. 56, 137-164 (1976).
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Cited in 1 Review
Cited in 7 Documents

MSC:

41A05 Interpolation in approximation theory
41A63 Multidimensional problems
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Full Text: DOI

References:

[1] Barnhill, R. E.; Birkhoff, G.; Gordon, W. J., Smooth interpolation in triangles, J. Approx. Theory, 8, 114-128 (1973) · Zbl 0271.41002
[2] Barnhill, R. E.; Mansfield, L., Error bounds for smooth interpolation in triangles, J. Approx. Theory, 11, 306-318 (1974) · Zbl 0286.41001
[3] Birkhoff, G., Tricubic polynomial interpolation, (Proc. Natl. Acad. Sci., 68 (1971)), 1162-1164 · Zbl 0242.41007
[4] Birkhoff, G., Interpolation to boundary data in triangles, J. Math. Anal. Appl., 42, 474-484 (1973) · Zbl 0262.41003
[5] Birkhoff, G.; Mansfield, L., Compatible triangular finite elements, J. Math. Anal. Appl., 47, 531-553 (1974) · Zbl 0284.35021
[6] Bramble, J. H.; Hilbert, S. R., Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation, SIAM J. Num. Anal., 7, 112-124 (1970) · Zbl 0201.07803
[7] Ciarlet, P. G.; Raviart, P. A., General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods, Arch. Rational Mech. Anal., 46, 177-199 (1972) · Zbl 0243.41004
[8] Ciarlet, P. G.; Wagschal, C., Multipoint Taylor formulas and applications to the finite element method, Numer. Math., 17, 84-100 (1971) · Zbl 0199.50104
[9] Irons, B. M., A conforming quartic triangular element for plate blending, Int. J. Numer. Methods Eng., 1, 29-45 (1969) · Zbl 0247.73071
[10] Mansfield, L., Higher order compatible triangular finite elements, Numer. Math., 22, 89-97 (1974) · Zbl 0265.65011
[11] Nicolaides, R. A., On a class of finite elements generated by Lagrange interpolation, II, SIAM J. Num. Anal., 10, 182-189 (1973) · Zbl 0244.65007
[12] Ženíšek, A., Interpolation polynomials on the triangle, Numer. Math., 15, 283-296 (1970) · Zbl 0216.38901
[13] Ženíšek, A., Hermite interpolation on simplexes in the finite element method, (Proceedings of the Czechoslovak Conference on Differential Equations and Their Applications. Proceedings of the Czechoslovak Conference on Differential Equations and Their Applications, Brno (1972)), 271-277 · Zbl 0347.65045
[14] Ženíšek, A., Polynomial approximation on tetrahedrons in the finite element method, J. Approx. Theory, 7, 334-351 (1973) · Zbl 0279.41005
[15] Ženíšek, A., Tetrahedral finite \(C^{(m)} \)-elements, (Acta Universitatis Carolinae—Mathematica et Physica (1974)), Nos. 1-2 · Zbl 0341.41001
[16] Zlámal, M., On the finite element method, Numer. Math., 12, 394-409 (1968) · Zbl 0176.16001
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