Object-oriented finite element programming is receiving recently more attention. In recent papers the authors' research group has developed systematically a methodology of coding finite elements within the context of an object-oriented paradigm, using successively several languages: Smalltalk, Ctalk and finally C⁺⁺.

The key features of the object-oriented approach : data encapsulation, message passing, hierarchical code organization, inheritance and polymorphism were shown to produce code with enhanced modularity, leading to faster prototyping of new code, better reusability even among different programmers, easier debugging, etc.

In this article an attempt to go beyond this stage is illustrated. The principles of object-oriented programming are applied directly to the problem statement in differential form.

The new approach proceeds as follows :

STRONG FORM, Stated by the user

Symbolic derivation : WEAK FORM

Symbolic derivation : GALERKIN FORM

Symbolic derivation : MATRIX FORM

Numerical derivation : NUMERICAL

MATRIX FORM

All derivations are carried out in symbolic form except for the final numerical matrix form. The barriers between symbolic and numerical programming are broken and code is generated automatically.

The potential of the proposed approach is illustrated at the example of linear elastodynamics.

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