Geodesic
Explicit estimation of error constants appearing in non-conforming linear triangular finite element method
Applications of Mathematics, Tome 63 (2018) no. 4, pp. 381-397.

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The non-conforming linear ($P_1$) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. 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 Babuška-Aziz maximum angle condition is required just as in the case of the conforming $P_1$ triangle. Some applications and numerical results are also included to see the validity and effectiveness of our analysis.
DOI : 10.21136/AM.2018.0097-18
Classification : 65N15, 65N30
Keywords: FEM; non-conforming linear triangle; a priori error estimate; a posteriori error estimate; error constant; Raviart-Thomas element 
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     title = {Explicit estimation of error constants appearing in non-conforming linear triangular finite element method},
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Liu, Xuefeng; Kikuchi, Fumio. Explicit estimation of error constants appearing in non-conforming linear triangular finite element method. Applications of Mathematics, Tome 63 (2018) no. 4, pp. 381-397. doi : 10.21136/AM.2018.0097-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0097-18/

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