Anisotropic modified Crouzeix-Raviart finite element method for the stationary Navier-Stokes equation

04/20/2023

∙

by   Hiroki Ishizaka, et al.

∙

0

∙

share

We study an anisotropic modified Crouzeix–Raviart finite element method to the rotational form of the stationary incompressible Navier–Stokes equation with large irrotational body forces. We present an anisotropic H^1 error estimate for the velocity of a modified Crouzeix–Raviart finite element method for the Navier–Stokes equation. The modified Crouzeix–Raviart finite element scheme was obtained using a lifting operator that maps the velocity test functions to H(÷;Ω)-conforming finite element spaces. Because no shape-regularity mesh conditions are imposed, anisotropic meshes can be used for analysis. The core idea of the proof involves using the relation between the Raviart–Thomas and Crouzeix–Raviart finite element spaces. Furthermore, we present a discrete Sobolev inequality under a semi-regular mesh condition to estimate the stability of the proposed method and confirm the obtained results through numerical experiments.