Mat-1.3656 Seminar on
numerical analysis and computational science
Monday Dec 1, 2008, room
U356 at 14.15, Eirola & Stenberg
Sergey Korotov, TKK Mat
The longest-edge bisection algorithm
We shall present the longest-edge bisection algorithm,
which chooses for bisection the longest edge in a given
face-to-face simplicial partition of a bounded polytopic
domain in $R^d$. Dividing this edge at its midpoint
we define a locally refined partition of all simplices
that surround this edge. Repeating this process,
we obtain a family $\mathcal F=\{\mathcal T_h\}_{h\to 0}$
of nested face-to-face partitions $\mathcal T_h$.
For $d=2$ we prove that this family is strongly regular, i.e.,
there exists a constant $C>0$ such that \meas $T\ge Ch^2$
for all triangles $T\in\mathcal T_h$ and all triangulations
$\mathcal T_h\in \mathcal F$. In particular,
the well-known minimum angle condition is valid.