Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methods
Kenta Kobayashi, Takuya Tsuchiya
TL;DR
This paper analyzes the error bounds of Crouzeix-Raviart and Raviart-Thomas finite element methods for 2D Poisson problems, providing geometric-independent estimates and confirming them through numerical experiments.
Contribution
It offers new error estimates that are independent of triangulation geometry, extending previous techniques to these finite element methods.
Findings
Error estimates independent of triangle shape
Numerical experiments confirm theoretical bounds
Applicable to lowest degree finite element methods
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 Babu\v{s}ka-Aziz and the authors. We present error estimates in terms of the circumradius and the diameter of triangles in which the constants are independent of the geometric properties of the triangulations. Numerical experiments confirm the results obtained.
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