Istituto di Scienza e Tecnologie dell'Informazione     
Caprili M., Cella A., Gheri G. Spline interpolation techniques for variational methods. In: International Journal for Numerical Methods in Engineering, vol. 6 pp. 565 - 576. John Wiley & Sons, 1973.
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 hyperelements, while high precision finite elements become convenient for very fine or irregular partition.

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