B.2.2 Rectangle

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u( $\displaystyle \xi$ , $\displaystyle \eta$ ) = $\displaystyle \alpha_{1}^{}$ + $\displaystyle \alpha_{2}^{}$ $\displaystyle \xi$ + $\displaystyle \alpha_{3}^{}$ $\displaystyle \eta$ + $\displaystyle \alpha_{4}^{}$ $\displaystyle \xi$ $\displaystyle \eta$

N₁( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	(1 - $\displaystyle \xi$ )(1 - $\displaystyle \eta$ )
N₂( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	$\displaystyle \xi$ (1 - $\displaystyle \eta$ )
N₃( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	$\displaystyle \xi$ $\displaystyle \eta$
N₄( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	$\displaystyle \eta$ (1 - $\displaystyle \xi$ )

$\resizebox{5.0cm}{!}{\includegraphics{/iue/a39/users/radi/diss/fig/shape/lin2Dq_2.eps}}$

u( $\displaystyle \xi$ , $\displaystyle \eta$ ) = $\displaystyle \alpha_{1}^{}$ + $\displaystyle \alpha_{2}^{}$ $\displaystyle \xi$ + $\displaystyle \alpha_{3}^{}$ $\displaystyle \eta$ + $\displaystyle \alpha_{4}^{}$ $\displaystyle \xi^{2}_{}$ +
$\displaystyle \alpha_{5}^{}$ $\displaystyle \xi$ $\displaystyle \eta$ + $\displaystyle \alpha_{6}^{}$ $\displaystyle \eta^{2}_{}$ + $\displaystyle \alpha_{7}^{}$ $\displaystyle \xi^{2}_{}$ $\displaystyle \eta$ + $\displaystyle \alpha_{8}^{}$ $\displaystyle \xi$ $\displaystyle \eta^{2}_{}$

N₁( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	(1 - $\displaystyle \xi$ )(1 - $\displaystyle \eta$ )(1 - 2 $\displaystyle \xi$ - 2 $\displaystyle \eta$ )
N₂( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	- $\displaystyle \xi$ (1 - $\displaystyle \eta$ )(1 - 2 $\displaystyle \xi$ + 2 $\displaystyle \eta$ )
N₃( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	- $\displaystyle \xi$ $\displaystyle \eta$ (3 - 2 $\displaystyle \xi$ - 2 $\displaystyle \eta$ )
N₄( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	- $\displaystyle \eta$ (1 - $\displaystyle \xi$ )(1 + 2 $\displaystyle \xi$ - 2 $\displaystyle \eta$ )
N₅( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	4 $\displaystyle \xi$ (1 - $\displaystyle \xi$ )(1 - $\displaystyle \eta$ )
N₆( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	4 $\displaystyle \xi$ $\displaystyle \eta$ (1 - $\displaystyle \eta$ )
N₇( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	4 $\displaystyle \xi$ $\displaystyle \eta$ (1 - $\displaystyle \xi$ )
N₈( $\displaystyle \xi$ , $\displaystyle \eta$ )	=	4 $\displaystyle \eta$ (1 - $\displaystyle \xi$ )(1 - $\displaystyle \eta$ )