
\subsection{\bf Conditions on Triangulation}

\begin{slide}

\begin{itemize}
\item You need nicely shaped triangles to ensure that
\[
\sum_{j\neq i} \left| S_{ij} \right| \leq \left| S_{ii} \right|
\]
for each $i$ (diagonal dominance)

\item This is satisfied if triangulation is such that $\theta_1 +
\theta_2 \leq 180^\circ$ for every internal edge $e$ (Figure~FEM~8a).

\vspace{5pt}
\begin{center}
\centerline{\psfig{figure=cps615.fig8a.ps,clip=true,width=3.75in}}
Figure: FEM 8a
\end{center}
\vspace{5pt}

\item Skinny triangles violate this!

\vspace{5pt}
\begin{center}
\centerline{\psfig{figure=cps615.fig8b.ps,clip=true,width=3.75in}}
Figure: FEM 8b
\end{center}
\end{itemize}

\end{slide}

