Error Analysis of the Nonconforming P1 Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations

Yanming Lai; Kewei Liang; Ping Lin; Xiliang Lu; Qimeng Quan

doi:10.4208/aam.OA-2023-0016

Error Analysis of the Nonconforming P₁ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations

Yanming Lai, Kewei Liang, Ping Lin, Xiliang Lu (Lead / Corresponding author), Qimeng Quan

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we investigate the nonconforming P₁ finite element approximation to the sequential regularization method for unsteady Navier-Stokes equations. We provide error estimates for a full discretization scheme. Typically, conforming P₁finite element methods lead to error bounds that depend inversely on the penalty parameter ϵ. We obtain an ϵ-uniform error bound by utilizing the {nonconforming P1} finite element method in this paper. Numerical examples are given to verify theoretical results.

Original language	English
Number of pages	29
Journal	Annals of Applied Mathematics
Early online date	4 Sept 2023
DOIs	https://doi.org/10.4208/aam.OA-2023-0016
Publication status	E-pub ahead of print - 4 Sept 2023

Keywords

Navier-Stokes equations
error estimates
finite element method
stabilization method

Access to Document

10.4208/aam.OA-2023-0016

Cite this

@article{0a10328ada0d4b19a31fd9e8f0632b9b,

title = "Error Analysis of the Nonconforming P1 Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations",

abstract = "In this paper we investigate the nonconforming P1 finite element approximation to the sequential regularization method for unsteady Navier-Stokes equations. We provide error estimates for a full discretization scheme. Typically, conforming P1 finite element methods lead to error bounds that depend inversely on the penalty parameter ϵ. We obtain an ϵ-uniform error bound by utilizing the {nonconforming P1} finite element method in this paper. Numerical examples are given to verify theoretical results.",

keywords = "Navier-Stokes equations, error estimates, finite element method, stabilization method",

author = "Yanming Lai and Kewei Liang and Ping Lin and Xiliang Lu and Qimeng Quan",

note = "Copyright: {\textcopyright} Global Science Press.",

year = "2023",

month = sep,

day = "4",

doi = "10.4208/aam.OA-2023-0016",

language = "English",

}

TY - JOUR

T1 - Error Analysis of the Nonconforming P1 Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations

AU - Lai, Yanming

AU - Liang, Kewei

AU - Lin, Ping

AU - Lu, Xiliang

AU - Quan, Qimeng

PY - 2023/9/4

Y1 - 2023/9/4

N2 - In this paper we investigate the nonconforming P1 finite element approximation to the sequential regularization method for unsteady Navier-Stokes equations. We provide error estimates for a full discretization scheme. Typically, conforming P1 finite element methods lead to error bounds that depend inversely on the penalty parameter ϵ. We obtain an ϵ-uniform error bound by utilizing the {nonconforming P1} finite element method in this paper. Numerical examples are given to verify theoretical results.

AB - In this paper we investigate the nonconforming P1 finite element approximation to the sequential regularization method for unsteady Navier-Stokes equations. We provide error estimates for a full discretization scheme. Typically, conforming P1 finite element methods lead to error bounds that depend inversely on the penalty parameter ϵ. We obtain an ϵ-uniform error bound by utilizing the {nonconforming P1} finite element method in this paper. Numerical examples are given to verify theoretical results.

KW - Navier-Stokes equations

KW - error estimates

KW - finite element method

KW - stabilization method

U2 - 10.4208/aam.OA-2023-0016

DO - 10.4208/aam.OA-2023-0016

M3 - Article

SN - 2096-0174

JO - Annals of Applied Mathematics

JF - Annals of Applied Mathematics

ER -