Two-dimensional Shape Functions
Shape functions are selected to fit as exact as possible the Finite Element Solution. If this solution is a combination of polynomial functions of pth order, these functions should include a complete polynomial of equal order.
That is, a complete polynomial of pth order can be written as:
can only fit polynomial functions of pth order if they content a polynomial function
for any polynomial function of pth order it is enough to use p-1 integration points.