On the Angle Condition in the Finite Element Method

The finite element procedure consists in finding an approximate solution in the form of piecewise linear functions, piecewise quadratic, etc. For two-dimensional problems, one of the most frequently used approaches is to triangulate the domain and find the approximate solution which is linear, quadratic, etc., in every triangle. A condition which is considered essential is that the angle of every triangle, independent of its size, should not be small. In this paper it is shown that the minimum angle condition is not essential. What is essential is the fact that no angle is too close to $180^ \circ $.