# Two-dimensional Shape Functions

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− | with <math>\ | + | with: <math>\qquad p=\frac{(n+1)(n+2)}{2}</math> the number of terms. |

## Revision as of 09:49, 4 November 2009

Shape functions are selected to fit as exact as possible the Finite Element Solution. If this solution is a combination of polynomial functions of n^{th} order, these functions should include a complete polynomial of equal order.

That is, a complete polynomial of n^{th} order can be written as:

with: the number of terms.

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.