OBJECT-ORIENTED FINITE-ELEMENTS-III - THEORY AND APPLICATION OF AUTOMATIC PROGRAMMING

In a first paper [1], the authors have developed the key features of a n object-oriented environment for the symbolic derivation of linear in itial-boundary-value problems. The approach was illustrated on a simpl e example of an elastic bar in dynamics. In a companion paper [2], the structure of the proposed environment was described at length. In thi s article. the key features of the automatic generation of finite elem ents in a symbolic object-oriented environment are given. A few exampl es of derivation and automatic programming are developed and numerical ly tested. First, a classical Galerkin formulation of Stoves flow is c ompared to a Galerkin least-squares stabilization formulation. Then, v arious stabilized formulations are tested on a simple scalar diffusion model equation.