# Cubic element of the Serendipity family

Zienkiewicz and Taylor (2000) [zienkiewicz2000v1] present a rectangular cubic element of the Serendipity family (in Chapter 8) which will be described here, focusing on its implementation using an isoparametric approach, i.e. the same approximation used for the geometry will be used to approximate the displacement field vector .

The element and the 12 nodes are shown in the figure below.

(Source code, png, hires.png, pdf)

The variables of are interpolated using:

where and represent the interpolation and the displacement vector at node . The interpolation function for the corner nodes are:

and for the middle nodes are:

The coordinates for each node