2023/04/20 by Hiroki Ishizaka, Ishizaka, Hiroki · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2304.10214
openalex publication_date 2023/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We studied an anisotropic modified Crouzeix--Raviart finite element method for the rotational form of a stationary incompressible Navier--Stokes equation with large irrotational body forces. We present an anisotropic H1 error estimate for the velocity of the 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 mapped 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 the 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 semi-regular mesh conditions to estimate the stability of the proposed method, and confirm the results obtained through numerical experiments.