Hierarchal finite elements and precomputed arrays

Two‐dimensional C° finite elements of arbitrary polynomial order are developed for a general functional which includes a least squares or potential energy functional as special cases. The elements are ‘hierarchal’ in the sense that the nodal variables for polynomial order p constitute a subset of the nodal variables for order p +1. It is shown that the elemental arrays for high polynomial order may be efficiently computed by using hierarchal elements together with precomputed arrays—i.e., arrays which are computed once, stored on permanent file, and then re‐used in all subsequent applications of the program. A number of example problems are solved. Comparisons are made of the relative efficiency of finite element convergergence with mesh refinement (polynomial order held fixed) and with increasing polynomial order (mesh held fixed). The latter approach is found superior.