Error bounds for smooth interpolation in triangles. (English) Zbl 0286.41001


41A05 Interpolation in approximation theory
41A63 Multidimensional problems
41A20 Approximation by rational functions
65D05 Numerical interpolation
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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[1] Barnhill, R.E; Birkhoff, G; Gordon, W.J, Smooth interpolation in triangles, J. approximation theory, 8, 114-128, (1973) · Zbl 0271.41002
[2] Barnhill, R.E; Gregory, J.A, Sard kernel theorems on triangular and rectangular domains with extensions and applications to finite element error bounds, () · Zbl 0276.65049
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[4] Birkhoff, G, Tricubic polynomial interpolation, (), 1162-1164 · Zbl 0242.41007
[5] {\scG. Birkhoff and L. Mansfield}, Compatible triangular finite elements, J. Math. Anal. Appl., to appear. · Zbl 0284.35021
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[7] Mansfield, L.E, Optimal approximation and error bounds in spaces of bivariate functions, J. approximation theory, 5, 77-96, (1972) · Zbl 0247.41012
[8] Sard, A, Linear approximation, (1963), American Mathematical Society Providence, R. I · Zbl 0115.05403
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