An Investigation of the Implementation of the p-Version Finite Element Method

The use of the p-version finite element method has become more widespread over the last five years or so, as witnessed by the addition of p-elements to a number of well known commercial codes. A review of the keynote papers on the p-version method is presented which focusses on the use of the hierarchical concept and the selection of the interpolation functions. The importance of accurate geometry mapping is also discussed, and the use of the blending function method is presented. Details of implementation of the p-version method are discussed in the light of the authors efforts to develop a program for solving two-dimensional elastostatic problems. Topics covered include the rules for numerical integration for the p-method, the possible use of numerical rather than explicit differentiation for determining the Jacobian matrix, and the programming of the load vector for the p-method. The lessons learnt are illustrated by simple examples, and will be of benefit to those wishing to program p-elements for other applications.