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Explicit estimation of error constants appearing in non-conforming linear triangular finite element method. (English) Zbl 06945738
Summary: 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.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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