Explicit Estimation of Error Constants Appearing in Non-conforming Linear Triangular Finite Element

TL;DR

This paper derives theoretical upper bounds for error constants in non-conforming linear triangular finite element methods, providing practical computational results and validating the analysis through numerical experiments.

Contribution

It introduces explicit estimates of error constants for non-conforming P1 triangular FEM, extending the understanding of error bounds in this context.

Findings

Derived upper bounds for error constants

Validated bounds through numerical experiments

Confirmed maximum angle condition applicability

Abstract

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.