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Spline interpolation techniques for variational methods
Author(s) -
Caprili M.,
Cella A.,
Gheri G.
Publication year - 1973
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620060412
Subject(s) - spline interpolation , mathematics , bicubic interpolation , nearest neighbor interpolation , hermite spline , cubic hermite spline , interpolation (computer graphics) , polyharmonic spline , thin plate spline , hermite interpolation , bilinear interpolation , monotone cubic interpolation , stairstep interpolation , trigonometric interpolation , spline (mechanical) , norm (philosophy) , multivariate interpolation , mathematical analysis , hermite polynomials , computer science , artificial intelligence , motion (physics) , statistics , structural engineering , law , political science , engineering
Interpolation techniques are reviewed in the context of the approximation of the solution of boundary value problems. From the variational formulation, the approximation error norm is related to the interpolation error norm. Among global interpolation techniques, bicubic splines and spline‐blended are reviewed; among local, Hermite's and ‘serendipity’ polynomials. The corresponding interpolation error norms are computed numerically on two test functions. The methods are compared for accuracy and for number of operations required in the solution of boundary value problems. The conclusion is that spline interpolation is most convenient for regular hyper‐elements, while high precision finite elements become convenient for very fine or irregular partition.