# Two-dimensional Shape Functions

(Difference between revisions)
 Revision as of 09:30, 4 November 2009 (view source)JMora (Talk | contribs) (New page: Category: Shape Functions) Revision as of 09:47, 4 November 2009 (view source)JMora (Talk | contribs) Newer edit → Line 1: Line 1: + 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: + + + :$f(x,y)=\sum_{i=1}^p \alpha_i x^j y^k; \qquad j+k \le p$ + + 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. + + + + + + + == References == + + # [http://en.wikipedia.org/wiki/Pascal%27s_triangle Pascal's triangle] [[Category: Shape Functions]] [[Category: Shape Functions]]

## Revision as of 09:47, 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 pth order, these functions should include a complete polynomial of equal order.

That is, a complete polynomial of pth order can be written as:

$f(x,y)=\sum_{i=1}^p \alpha_i x^j y^k; \qquad j+k \le p$

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.

## References

1. Pascal's triangle