Explicit Estimation of Error Constants Appearing in Non-conforming Linear Triangular Finite Element
Provides quantitative error bounds for non-conforming FEM, which is incremental for researchers in numerical analysis.
The paper derives theoretical upper bounds and computational results for error constants in non-conforming linear triangular FEM, showing that the Babuška-Aziz maximum angle condition is required. Numerical results validate the analysis.
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.