Keywords: finite element methods, shells, MITC elements, transient dynamics, explicit and implicit methods, large eigenvalue problems, modelling of proteins and DNA structures..

In this chapter, we consider some frontiers in finite element procedures, and frontiers of novel applications. We focus on theoretically well-founded procedures that advance the solution of practical problems in engineering and the sciences. For the analysis of shells, the use of interpolation covers to enhance solutions is presented and the new MITC3+ shell element is discussed. For transient dynamic solutions, insights in implicit and explicit time integration methods and the solution of large eigenvalue problems are given. For multi-physics analyses, the full coupling between solid, fluid, electromagnetic, and thermal effects is considered. Finally, we also briefly focus on the finite element modelling of Protein and DNA nano-scale structures by coarse graining, which represents a very important frontier for future research.

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