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]]

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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.

References

1. Pascal's triangle