# Two-dimensional Shape Functions

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+ | 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<sup>th</sup> order, these functions should include a complete polynomial of equal order. | ||

+ | That is, a complete polynomial of p<sup>th</sup> order can be written as: | ||

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+ | :<math>f(x,y)=\sum_{i=1}^p \alpha_i x^j y^k; \qquad j+k \le p</math> | ||

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+ | can only fit polynomial functions of p<sup>th</sup> order if they content a polynomial function | ||

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

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+ | == References == | ||

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+ | # [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 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.