In the following a simple example shall show the determination of linear approximation functions for a rectangular element.

A simple rectangle is chosen for the elements because the approximation functions are functions of the geometry of the element.

The sides of the elements in direction of the x and y-axis have the length *a *and *b* respectively.

Additionally, a local coordinate system is defined that has its origin in the vertex 1 (see figure to the right).

The introduction of the local coordinate system is a first taste of the coordinate transformation and the so-called master element that will be explained in chapter 3.1.6.