  We discuss the error analysis of the lowest degree Crouzeix-Raviart and
Raviart-Thomas finite element methods applied to a two-dimensional Poisson
equation. To obtain error estimations, we use the techniques developed by
Babu\v{s}ka-Aziz and the authors. We present error estimates in terms of the
circumradius and the diameter of triangles in which the constants are
independent of the geometric properties of the triangulations. Numerical
experiments confirm the results obtained.
