Symbolic object-oriented Finite Element Programming Application to incompressible viscous flow

The object-oriented approach applied to the Finite Element Method leads to better structured numerical codes. The purpose of such an approach is to facilitate the maintenance and the extension of the code. Among the early work in this domain one may note [1] [2], the authors’ contribution in [3] [4] [5]. After this work, which was restricted to the direct coding of the matrix form, an object-oriented approach applied to the symbolic derivations of Finite Element models and automatic programming was proposed [6] [7]. Many attempts in this domain already exist ([8] [9] [10] [11] for example), but they were restricted to the derivation of specific elemental matrices. The advantage of using the high level of abstraction of Object-Oriented Programming is that it leads, on one hand to an environment which is easy to extend, and on the other hand to quite natural derivations. Simple applications in linear mechanics were shown in references [7] and [12]. The present paper introduces a first extension of the environment to non-linear mechanics; a simple model of Navier-Stokes flow illustrates the new approach.