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revision 4344 by jfenwick, Wed Feb 27 03:42:40 2013 UTC revision 4345 by jfenwick, Fri Mar 29 07:09:41 2013 UTC
# Line 48  where Line 48  where
48  \fracp{y_{i}}{u_{k}} v_{i}\delta_{k} \; ds  \fracp{y_{i}}{u_{k}} v_{i}\delta_{k} \; ds
49  \end{equation}  \end{equation}
50  It is assumed that the initial guess $u^{(0)}$ fulfills the constraint~(\ref{APP NEWTON EQU 40b}).  It is assumed that the initial guess $u^{(0)}$ fulfills the constraint~(\ref{APP NEWTON EQU 40b}).
51  The $\delta^{(\nu-1)}$ has to fullfill the homogeneous constraint.  The $\delta^{(\nu-1)}$ has to fulfill the homogeneous constraint.
52  Notice that the calculation of $\delta^{(\nu-1)}$ requires the solution of a linear PDE  Notice that the calculation of $\delta^{(\nu-1)}$ requires the solution of a linear PDE
53  as presented in section~\ref{SEC LinearPDE}.  as presented in section~\ref{SEC LinearPDE}.
54    
# Line 192  following Newton-Raphson correction, see Line 192  following Newton-Raphson correction, see
192  mean that no digits should be computed which are in significance  mean that no digits should be computed which are in significance
193  below the prescribed tolerance {\it rtol}.  The number $0.1$ is a `safety factor' to take care  below the prescribed tolerance {\it rtol}.  The number $0.1$ is a `safety factor' to take care
194  of the coarse norm estimations. Figure~\ref{APP NEWTON PIC 61} shows the workflow of  of the coarse norm estimations. Figure~\ref{APP NEWTON PIC 61} shows the workflow of
195  the Newton-Raphson update aglorithm.  the Newton-Raphson update algorithm.
196    
197  \begin{figure}  \begin{figure}
198  \begin{center}  \begin{center}
# Line 258  the Newton-Raphson update aglorithm. Line 258  the Newton-Raphson update aglorithm.
258    \put(120,185){\vector(0,1){20}}    \put(120,185){\vector(0,1){20}}
259    
260  \put(20,145){\framebox(60,15){\parbox{48mm}  \put(20,145){\framebox(60,15){\parbox{48mm}
261             {evaluate stopping criterions~(\ref{APP NEWTON EQU 65})  \\             {evaluate stopping criteria~(\ref{APP NEWTON EQU 65})  \\
262             and if not simplified mode~(\ref{APP NEWTON EQU 66}) } } }             and if not simplified mode~(\ref{APP NEWTON EQU 66}) } } }
263  \put(50,145){\vector(0,-1){10}}  \put(50,145){\vector(0,-1){10}}
264    

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