An object-oriented hybrid symbolic/numerical approach for the development of finite element codes

The association of object-oriented programming and symbolic computation techniques introduces certain changes in finite element code organization. The purpose of this approach is to speed up the design of new formulations. Previous papers have described the basic concepts of the method. In this paper, the focus is placed on functional aspects of symbolic tools for the development of finite element formulations. Two practical examples are used to illustrate this point. The first is a space-time formulation for an incompressible flow driven by the Navier–Stokes equations, and the second is a finite element derivation of the total potential energy for linear elasticity.