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 p^th order, these functions should include a complete polynomial of equal order.

That is, a complete polynomial of p^th order can be written as:

can only fit polynomial functions of p^th order if they content a polynomial function

for any polynomial function of pth order it is enough to use p-1 integration points.

References

1. Pascal's triangle