Mixed Methods for the Stress-Displacement Formulation of Elasticity - A Software Framework for Advanced Finite Elements Methods

Recently, Winther et. al. have developed several finite element methods for the mixed formulation of elasticity. These methods have attracted considerable attention internationally, but have only been implemented in 2D. One of the goals in this project i s to implement them in 3D. Notice that these elements are rather complicated compared to standard finite elements (this is further explained in the project description). Mardal (together with Langtangen) has developed many of the tools for advanc ed finite elements in Diffpack. Based on this experience, we emphasize that the effort of implementing these mixed methods should not be underestimated. In fact, we argue that the complexity of these elements challenges the usual way to implement fi nite element methods. Therefore, we will develop a general finite element package on top of a symbolic mathematics library for polynomials (GiNaC). With this package one should be able to work with polynomials and polynomial spaces symbolically and he reby define finite elements as they are defined mathematically. The package will be open source and will be coupled to other packages for mesh generation (e.g. NetGen) and linear algebra (e.g. Trilinos).