Common and unusual finite elements

Abstract

This chapter provides a glimpse of the considerable range of finite elements in the literature. Many of the elements presented here are implemented as part of the FEniCS project already; some are future work. The universe of finite elements extends far beyond what we consider here. In particular, we consider only simplicial, polynomial-based elements. We thus bypass elements defined on quadrilaterals and hexahedra, composite and macro-element techniques, as well as XFEM-type methods. Even among polynomial-based elements on simplices, the list of elements can be extended. Nonetheless, this chapter presents a comprehensive collection of some the most common, and some more unusual, finite elements.