 # Finite Element Method (FEM) Figure 1: Rectangular and triangular Lagrangian element with linear approximation function, taken from [*1]. Figure 2: Rectangular and triangular Lagrangian element with square approximation function, taken from [*1].

## The approximation functions (5)

The approximation functions for selected master elements (see Fig. 1 and Fig. 2) are given now as a preview of what is to come in "Numerical Integration".

For example, the coordinate transformation and the introduction of the so-called master element. How the latter are motivated and derived can be found in respective technical literature. The choice of the approximation functions is based on their use in the finite element program RMA2. Some of these approximation functions will serve as examples too.

In general, the difference between approximation functions is in their order, i.e. they are linear, square or of a higher order, and furthermore they are different in the applied element shape (geometry). All of these factors determine the necessary sampling rate or vertex count that defines how the function distributes over the element.  