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Japan Journal of Industrial and Applied Mathematics

, Volume 35, Issue 3, pp 1191–1211 | Cite as

Error analysis of Crouzeix–Raviart and Raviart–Thomas finite element methods

  • Kenta Kobayashi
  • Takuya TsuchiyaEmail author
Original Paper Area 2

Abstract

We discuss the error analysis of the lowest degree Crouzeix–Raviart and Raviart–Thomas finite element methods applied to a two-dimensional Poisson equation. To obtain error estimations, we use the techniques developed by Babuška–Aziz and the authors. We present error estimates in terms of the circumradius and diameter of triangles in which the constants are independent of the geometric properties of the triangulations. Numerical experiments confirm the results obtained.

Keywords

Crouzeix–Raviart Raviart–Thomas Finite element method Error estimation Triangulation Circumradius 

Mathematics Subject Classification

65D05 65N30 

Notes

Acknowledgements

The authors were supported by JSPS KAKENHI Grant Numbers JP26400201, JP16H03950, and JP17K18738. The authors thank the anonymous referee for the valuable comments that helped to improve this paper.

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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Commerce and ManagementHitotsubashi UniversityKunitachiJapan
  2. 2.Graduate School of Science and EngineeringEhime UniversityMatsuyamaJapan

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