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

Xuefeng Liu; Fumio Kikuchi

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arXiv · 1805.10591

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

Xuefeng Liu·Fumio Kikuchi

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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.

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Xuefeng Liu, Fumio Kikuchi. 2018-05-27. Explicit Estimation of Error Constants Appearing in Non-conforming Linear Triangular Finite Element. https://arxiv.org/abs/1805.10591

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