Once the physical problem is taken into account properly, the major concern of the engineer is reliability of the numerical code, and cost and delay to run an application. The growing need of very complicated problems, for which meshing “by hand” is less and less thinkable, urged the development of friendly automatic meshing and remeshing tools.

In contrast, it is now possible to evaluate quantitatively the confidence we can put into an actual computation with the a posteriori error estimation. The combination of both approaches has been achieved: after a first trial computation, the most advanced methodology permits us to generate a new mesh automatically, which is locally refined in order that the error is always below an acceptable value for practical purpose.

Finally, when very large problems are in three dimensions, both computer time and memory allocation may become prohibitive. This concern can be taken into account by utilizing iterative methods for solving large linear systems, in order to save computer time, reduce the memory requirement, and facilitate the optimal use of parallel computers.

Meshing and Remeshing

The meshing capability of a FE code is now very important, as the manual generation of the complex meshes that are treated is almost impossible and always dissuading. When the incremental simulation of a forming sequence is considered, automatic remeshing is still more important. We shall briefly review the main methods for meshing and discuss their possible generalization to remeshing.