A general approach to transforming finite elements
This work addresses a long-standing implementation bottleneck for non-affine-equivalent finite elements, which is important for computational mechanics and numerical analysis.
The paper introduces a generalized mapping approach for finite elements that lack standard reference element equivalence, enabling efficient implementation of Hermite, Morley, Argyris, and Bell elements in finite element codes.
The use of a reference element on which a finite element basis is constructed once and mapped to each cell in a mesh greatly expedites the structure and efficiency of finite element codes. However, many famous finite elements such as Hermite, Morley, Argyris, and Bell, do not possess the kind of equivalence needed to work with a reference element in the standard way. This paper gives a generalizated approach to mapping bases for such finite elements by means of studying relationships between the finite element nodes under push-forward.