  The non-conforming linear ($P_1$) triangular FEM can be viewed as a kind of
the discontinuous Galerkin method, and is attractive in both theoretical and
practical senses. Since various error constants must be quantitatively
evaluated for its accurate a priori and a posteriori error estimates, we derive
their theoretical upper bounds and some computational results. In particular,
the Babu$\check{s}$ka-Aziz maximum angle condition is required just as in the
case of the conforming $P_1$ triangle. Some applications and numerical results
are also illustrated to see the validity and effectiveness of our analysis.
