Abstrakt
The well-known maximum angle condition, [3], gives us O(h) convergence of the piecewise linear finite element method. In [2], it is shown by a simple argument, that this condition is not necessary, only sufficient.
While the necessary and sufficient condition remains unknown, we generalize the maximum angle condition, so that degenerating elements are allowed, as long as they form clusters of diameter at most O(h) which are at least O(h) apart.