Object-oriented finite elements. IV. Symbolic derivations and automatic programming of nonlinear formulations Original Research Article

In previous papers [Comput. Methods Appl. Mech. Eng. 132 (1996) 277–304, 259–276; 154 (1998) 41–68] , the authors have presented the main ideas, which have led to the creation of an environment for symbolic derivations of variational problems and automatic programming of finite elements codes. In these papers, only linear formulations were treated, e.g., Galerkin formulation for elastodynamics [Adv. Eng. Soft. 27 (1996) 3–10] or Galerkin least-squares (GLS) formulation of Stokes flow problem. In this paper, we wish to show a natural extension of symbolic derivation concepts to nonlinear formulations, using the general notion of directional derivative. The application to the numerical solution of Navier–Stokes equations is given.