English

Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition

Numerical Analysis 2020-10-08 v2 Numerical Analysis

Abstract

We investigate the piecewise linear nonconforming Crouzeix-Raviar and the lowest order Raviart-Thomas finite-element methods for the Poisson problem on three-dimensional anisotropic meshes. We first give error estimates of the Crouzeix-Raviart and the Raviart-Thomas finite-element approximate problems. We next present the equivalence between the Raviart-Thomas finite-element method and the enriched Crouzeix-Raviart finite-element method. We emphasise that we do not impose either shape-regular or maximum-angle condition during mesh partitioning. Numerical results confirm the results that we obtained.

Keywords

Cite

@article{arxiv.2006.00631,
  title  = {Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition},
  author = {Hiroki Ishizaka and Kenta Kobayashi and Takuya Tsuchiya},
  journal= {arXiv preprint arXiv:2006.00631},
  year   = {2020}
}

Comments

29 pages, 3 figures