Reference element. Notion of curved finished element
Overview of the finite element method

All the elements introduced in the previous paragraphs had simple geometric forms, for example, in dimension two, triangles or squares; in practice, we have to use elements with more elaborate forms, in particular any triangles or quadrilaterals or with curved sides to best approximate the $\partial \mathrm{\Omega }$ boundary, when the $\mathrm{\Omega }$ domain is not polyhedral.

The aim of this paragraph is to show how, by using certain transformations, we can obtain elements with a more complicated geometry. In addition, these transformations make it possible to calculate integrals not on the current element K, but on a reference element xml...