Symbolic Derivation of Equations for Mixed Formulation in Finite Element Analysis

One important application area of symbolic manipulation systems is to use them as preprocessors to generate numerical code for target machines, thus facilitating the tedious pre-processing involved in numerical computing, particularly in Finite Element Method (FEM). However, pre-processing the given formulation often generates unacceptable results due to the number of derivation steps involved as well as the exponential growth of expressions produced. Presented in this paper are some of the procedures and techniques we have developed for efficient derivation of element equations in FEM. Examples are given for applications of those procedures and techniques in the derivation of element equations for mixed formulations.