Istituto di Scienza e Tecnologie dell'Informazione     
Cella A. Approximation techniques in the finite element method. Presented at the Course on Finite Elements, Centre Internationelle des Sciences Mechaniques, Udine, July 1972. Internal note IEI-B72-11, 1972.
The numerical solution of boundary value problems by the finite element method is based on three major steps: the existence of a suitable variational formulation, the approximation of the solution space, the numerical solution of a set of linear equations. The purpose here is to review the well-known polynomial interpolation techniques currently used in the finite element method and to compare them to more recent spline interpolation methods. Among the latter, bicubic spline [3] and spline blended (14] interpolation were chosen because of the combination of accuracy and simplicity of computation offered. The evaluation of efficiency is based on the interpolation error and on the number of operations required, in the finite element method, to solve the corrisponding set of linear equation. Asymptotic error bounds are established from different assumptions on the nature and on the data of the boundary value problem. The present work collects and sintherizes part of the research work on approximation techniques under way at Istituto di Elaborazione dell'Informazione [7)[8] [5].

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