A new type of mesh inconsistency, called a ``deadlock'' (see Figure 15)
may occur. This occurs when an element cannot be refined in any direction
due to regularity requirements in each direction. Refining such
elements requires special logic to resolve the inconsistency, as the
simple recursive technique used in two-dimensional meshes and
three-dimensional isotropic meshes is not sufficient for these cases.
Moreover, while resolving the deadlock, the mesh is temporarily
inconsistent.
It is then possible to encounter another deadlock (``deadlock on a
deadlock'') and
refinement cannot proceed. As the mesh is inconsistent, all changes
must then be
reversed, necessitating a complicated tracking process. Deadlock
on a deadlock is not an uncommon situation, especially on big meshes
(
nodes). Deadlock correction procedures are very complicated (involving several
special cases), and we will not present them here in detail.
Figure 15: Typical mesh deadlock: middle element cannot be refined