Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methods
For numerical analysts working on finite element methods, this offers refined error bounds that are geometry-independent, though the approach is incremental.
The paper provides error estimates for Crouzeix-Raviart and Raviart-Thomas finite element methods for the 2D Poisson equation, with constants independent of triangle geometry, validated by numerical experiments.
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 the diameter of triangles in which the constants are independent of the geometric properties of the triangulations. Numerical experiments confirm the results obtained.