Object-oriented finite elements III. Theory and application of automatic programming

In a first paper [1], the authors have developed the key features of an object-oriented environment for the symbolic derivation of linear initial-boundary-value problems. The approach was illustrated on a simple example of an elastic bar in dynamics. In a companion paper [2], the structure of the proposed environment was described at length. In this article, the key features of the automatic generation of finite elements in a symbolic object-oriented environment are given. A few examples of derivation and automatic programming are developed and numerically tested. First, a classical Galerkin formulation of Stokes flow is compared to a Galerkin least-squares stabilization formulation. Then, various stabilized formulations are tested on a simple scalar diffusion model equation.