# Parametric interpolation for a cubic function

From KratosWiki

- For a function , it is known the values for 3 points:

- For a three nodes quadratic element, the interpolation of such function is:

- For this quadratic approach, the resulting expression is:

- and then:

- The following picture shows the error, much bigger outside of the interval.

- If the set of points is:
- that means:

- For the four nodes cubic element, the interpolation of such function is:

- Remember the expression to obtain each :

- therefore:

- The resulting expression is exactly the same to the original one: