Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations

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.

Author Details

Yanming Lai

Kewei Liang

Ping Lin

Xiliang Lu

Qimeng Quan