Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations
Year: 2024
Author: Yanming Lai, Kewei Liang, Ping Lin, Xiliang Lu, Qimeng Quan
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 1 : pp. 43–70
Abstract
In this paper we investigate the nonconforming $P_1$ finite element approximation to the sequential regularization method for unsteady Navier-Stokes equations. We provide error estimates for a full discretization scheme. Typically, conforming $P_1$ finite element methods lead to error bounds that depend inversely on the penalty parameter $\epsilon.$ We obtain an $\epsilon$-uniform error bound by utilizing the nonconforming $P_1$ finite element method in this paper. Numerical examples are given to verify theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2023-0016
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 1 : pp. 43–70
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Navier-Stokes equations error estimates finite element method stabilization method.