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Applications of Mathematics

, Volume 63, Issue 4, pp 381–397 | Cite as

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

  • Xuefeng Liu
  • Fumio Kikuchi
Article
  • 20 Downloads

Abstract

The non-conforming linear (P1) 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 P1 triangle. Some applications and numerical results are also included to see the validity and effectiveness of our analysis.

Keywords

FEM non-conforming linear triangle a priori error estimate a posteriori error estimate error constant Raviart-Thomas element 

MSC 2010

65N15 65N30 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Graduate School of Science and TechnologyNiigata UniversityNiigata City, NiigataJapan
  2. 2.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

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