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On completeness of shape functions for finite element analysis
Author(s) -
Taylor Robert L.
Publication year - 1972
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.1620040105
Subject(s) - interpolation (computer graphics) , finite element method , mathematics , completeness (order theory) , polygon mesh , computation , quadratic equation , polynomial interpolation , polynomial , simple (philosophy) , linear interpolation , algorithm , mathematical analysis , geometry , computer science , computer graphics (images) , animation , physics , thermodynamics , philosophy , epistemology
Some elements commonly used for analysis are examined for examined for completeness of polynomial interpolation and computational efficiency. Extensions to n ‐dimensional space are shown to be natural consequences of the interpolation, thus all elements considered here allow for finite element approximation in higher than three‐dimensional spaces (e.g. space–time interpolations). From the study it is concluded that ‘serendipity’ class elements from the most efficient elements up to third‐degree polynomial approximations. The method used here to develop the serendipity shape functions allows for different orders of interpolation along each edge. Thus, in zones where high accuracy is required meshes can now be easily changed from linear to quadratic or higher‐order elements. Computations on some simple problems have demonstrated this to be a superior method than using large numbers of low ordered elements.