\batchmode
\documentclass{article}
\usepackage{epsfig}
\usepackage{/home/cuvelier/Travail/Recherch/Matlab/FEM2Dtoolbox/OptFEM2DP1/doxygen/latexextras}
\pagestyle{empty}
\begin{document}
$ P_1 $
\pagebreak

$ \StiffElas $
\pagebreak

\[ \StiffElas_{m,l}=\int_{\DOMH} \Odv^t(\BasisFuncTwoD_m) \Ocv(\BasisFuncTwoD_l)dT, \ \forall (m,l)\in\ENS{1}{2\,\nq}^2,\]
\pagebreak

$ \BasisFuncTwoD_m $
\pagebreak

$ \Ocv=(\Occ_{xx},\Occ_{yy},\Occ_{xy})^t $
\pagebreak

$ \Odv=(\Odc_{xx},\Odc_{yy},2\Odc_{xy})^t $
\pagebreak

$ \Masse $
\pagebreak

\[ \Masse_{i,j}=\int_\DOMH \FoncBase_i(\q)\, \FoncBase_j(\q)\, d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2 \]
\pagebreak

$ \FoncBase_i $
\pagebreak

$ \MasseF{w} $
\pagebreak

\[ \MasseF{w}_{i,j}=\int_\DOMH w(\q)\FoncBase_i(\q) \FoncBase_j(\q) d\q,\ \forall (i,j)\in\ENS{1}{\nq}^2 \]
\pagebreak

$ \Stiff $
\pagebreak

\[ \Stiff_{i,j}=\int_\DOMH \DOT{\GRAD\FoncBase_i(\q)}{\GRAD\FoncBase_j(\q)}d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2\]
\pagebreak

$2\times\nq$
\pagebreak

${\q}(\il,j)$
\pagebreak

$\il$
\pagebreak

$j$
\pagebreak

$\il\in\{1,2\}$
\pagebreak

$j\in\ENS{1}{\nq}$
\pagebreak

$3\times\nme$
\pagebreak

$\me(\jl,k)$
\pagebreak

$\jl$
\pagebreak

$k$
\pagebreak

$\q$
\pagebreak

$\jl\in\{1,2,3\}$
\pagebreak

$k\in{\ENS{1}{\nme}}$
\pagebreak

$1\times\nq$
\pagebreak

$1\times\nme$
\pagebreak

$2\times\nbe$
\pagebreak

$\be(\il,l)$
\pagebreak

$l$
\pagebreak

$l\in{\ENS{1}{\nbe}}$
\pagebreak

$1\times\nbe$
\pagebreak

$\nq$
\pagebreak

$\nme$
\pagebreak

$\nbe$
\pagebreak

$lbe(j)$
\pagebreak

$\lbe(j)$
\pagebreak

$[0,1]\times[0,1]$
\pagebreak

$y=0$
\pagebreak

$x=1$
\pagebreak

$y=1$
\pagebreak

$x=0$
\pagebreak

$P_1$
\pagebreak

$3\times 3$
\pagebreak

\[AElem=\frac{area}{12}\left( \begin{array}{ccc} 2 &1 &1 \\ 1 &2 &1 \\ 1 &1 &2 \end{array} \right)\]
\pagebreak

$3\times 1$
\pagebreak

\[C=\left\{\begin{array}[ccc] &\lambda+2\mu &\lambda &0\\ &\lambda &\lambda+2\mu &0\\ &0 &0 &\mu \end{array} \right.\]
\pagebreak

$2\times 1$
\pagebreak

$\Masse$
\pagebreak

\[\Masse_{i,j}=\int_\DOMH \FoncBase_i(\q)\, \FoncBase_j(\q)\, d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2\]
\pagebreak

$\FoncBase_i$
\pagebreak

$\nq\times\nq$
\pagebreak

$\MasseF{w}$
\pagebreak

\[\MasseF{w}_{i,j}=\int_\DOMH w(\q)\FoncBase_i(\q) \FoncBase_j(\q) d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2\]
\pagebreak

$w$
\pagebreak

$Tw(i)=w(\q^i),$
\pagebreak

$\forall i\in\ENS{1}{\nq}$
\pagebreak

$\Stiff$
\pagebreak

\[\Stiff_{i,j}=\int_\DOMH \DOT{\GRAD\FoncBase_i(\q)}{\GRAD\FoncBase_j(\q)}d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2\]
\pagebreak

\[\StiffElas_{m,l}=\int_{\DOMH} \Odv^t(\BasisFuncTwoD_m) \Ocv(\BasisFuncTwoD_l)dT, \ \forall (m,l)\in\ENS{1}{2\,\nq}^2,\]
\pagebreak

$\BasisFuncTwoD_m$
\pagebreak

$\Ocv=(\Occ_{xx},\Occ_{yy},\Occ_{xy})^t$
\pagebreak

$\Odv=(\Odc_{xx},\Odc_{yy},2\Odc_{xy})^t$
\pagebreak

$2\nq\times 2\nq$
\pagebreak

$36\times \nme$
\pagebreak

\[\Masse_{i,j}=\int_\DOMH \FoncBase_i(\q) \FoncBase_j(\q) d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2\]
\pagebreak

\[\MasseF{w}_{i,j}=\int_\DOMH w(\q)\;\FoncBase_i(\q)\; \FoncBase_j(\q)\; d\q,\ \forall (i,j)\in{\ENS{1}{\nq}}^2\]
\pagebreak

\[\Masse_{i,j}=\int_\DOMH \FoncBase_i(\q) \FoncBase_j(\q) d\q,\ \forall (i,j)\in\ENS{1}{\nq}^2\]
\pagebreak

\[\int_\DOM u(x,y) v(x,y) dxdy \approx \DOT{\Masse \vecb{U}}{\vecb{V}}\]
\pagebreak

$\vecb{U}_i=u(\q^i)$
\pagebreak

$\vecb{V}_i=v(\q^i)$
\pagebreak

$u$
\pagebreak

$v$
\pagebreak

\[|\int_\DOM u\,v -\Pi_h(u)\,\Pi_h(v)d\DOM| \leq C h^2\]
\pagebreak

\[\MasseF{w}_{i,j}=\int_\DOMH w(\q)\FoncBase_i(\q) \FoncBase_j(\q) d\q,\ \forall (i,j)\in\ENS{1}{\nq}^2\]
\pagebreak

\[\int_\DOM w(x,y) u(x,y) v(x,y) dxdy \approx \DOT{\MasseF{w} \vecb{U}}{\vecb{V}}\]
\pagebreak

\[|\int_\DOM u\,v\,w -\Pi_h(u)\,\Pi_h(v)\,\Pi_h(w)d\DOM| \leq C h^2\]
\pagebreak

\[\Stiff_{i,j}=\int_\DOMH \DOT{\GRAD\FoncBase_i(\q)}{\GRAD\FoncBase_j(\q)}d\q,\ \forall (i,j)\in\ENS{1}{\nq}^2\]
\pagebreak

\[\int_\DOM \DOT{\GRAD u(\q)}{\GRAD v(\q)}d\q \approx \DOT{\Stiff \vecb{U}}{\vecb{V}}\]
\pagebreak

\[|\int_\DOM \DOT{\GRAD u}{\GRAD v} -\DOT{\GRAD \Pi_h(u)}{\GRAD \Pi_h(v)}d\DOM| \leq C h^2\]
\pagebreak

\[\int_\DOM \Odv^t(\vecb{u}) \Ocv(\vecb{v})d\q \approx \DOT{\StiffElas \vecb{U}}{\vecb{V}}\]
\pagebreak

$\foncdefsmall{\vecb{u}=(u_1,u_2)}{\DOM}{\R^2}$
\pagebreak

$\foncdefsmall{\vecb{v}=(v_1,v_2)}{\DOM}{\R^2}$
\pagebreak

$\vecb{U}_{2i-1}=u_1(\q^i),$
\pagebreak

$\vecb{U}_{2i}=u_2(\q^i),$
\pagebreak

$\vecb{V}_{2i-1}=v_1(\q^i),$
\pagebreak

$\vecb{V}_{2i}=v_2(\q^i)$
\pagebreak

$\vecb{U}_{i}=u_1(\q^i),$
\pagebreak

$\vecb{U}_{i+\nq}=u_2(\q^i),$
\pagebreak

$\vecb{V}_{i}=v_1(\q^i),$
\pagebreak

$\vecb{V}_{i+\nq}=v_2(\q^i)$
\pagebreak

$\vecb{u}$
\pagebreak

\[|\int_\DOM \Odv^t(\vecb{u}) \Ocv(\vecb{v})d\q - \DOT{\StiffElas \vecb{U}}{\vecb{V}}| \leq C h^2\]
\pagebreak

$\LaTeX{}$
\pagebreak

\[\mbox{\input{\INPUTLATEXDIR/benchMatlabR2012b_MassP1.tex}} \]
\pagebreak

\[\mbox{\input{\INPUTLATEXDIR/benchMatlabR2012b_MassWP1.tex}} \]
\pagebreak

\[\mbox{\input{\INPUTLATEXDIR/benchMatlabR2012b_StiffP1.tex}} \]
\pagebreak

\[\mbox{\input{\INPUTLATEXDIR/benchMatlabR2012b_StiffElasP1.tex}} \]
\pagebreak

\[\mbox{\input{\INPUTLATEXDIR/benchOctave3.6.3_MassP1.tex}} \]
\pagebreak

\[\mbox{\input{\INPUTLATEXDIR/benchOctave3.6.3_MassWP1.tex}} \]
\pagebreak

\[\mbox{\input{\INPUTLATEXDIR/benchOctave3.6.3_StiffP1.tex}} \]
\pagebreak

\[\mbox{\input{\INPUTLATEXDIR/benchOctave3.6.3_StiffElasP1.tex}} \]
\pagebreak

\end{document}
