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 Babuv{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.
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