Error analysis of Crouzeix–Raviart and Raviart–Thomas finite element methods
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.
KeywordsCrouzeix–Raviart Raviart–Thomas Finite element method Error estimation Triangulation Circumradius
Mathematics Subject Classification65D05 65N30
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.
- 6.Grisvard, P.: Elliptic Problems in Nonsmooth Domains, Pitman, 1985, reprinted by SIAM (2011)Google Scholar
- 7.Kikuchi, F.: Mathematics of the Finite Element Methods, (in Japanese) Baifu-kan (1996)Google Scholar
- 8.Kikuchi, F., Saito, N.: Principle of Numerical Analysis (in Japanese), Iwanami-Shoten (2016)Google Scholar
- 13.Liu, X., Kikuchi, F.: Estimation of error constants appearing in non-conforming linear triangular finite element, Proceedings of APCOM’07-EPMESC XI (2007)Google Scholar