The complete basises of the bicubic finite element
Authors: J. I. Nikolaenko, S. V. Moiseenko, O. A. Samoylenko
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The work is dedicated to building the broadest family of basises of bicubic finite element and the allocation of its quasi-harmonic basises. The five-parameter family of complete basises and threeparameter family of bicubic finite element basises, complete with respect to all harmonic polynomials up to the third degree inclusive were built. Two quasi-harmonic basises that accurately approximate the harmonic functions were extracted from the three-parameter family. Mandatory conditions such as: the function of its site is one, in otherwise - zero, were used in the construction of the basis functions in the form of bicubic polynomials. Completeness condition was added to these conditions, which provides an accurate approximation of linear functions, as well as the symmetry (geometry) finite element was taken into account. The sum of squared deviations Laplacians values of basis functions from zero was taken as an additional measure of the basis functions harmony. Relative error, meansquare deviation, the Gram matrix of these bases and the condition number were calculated for comparison of properties of considered basises.