Fumio Kikuchi

Xuefeng Liu, Fumio Kikuchi

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.