Volume 40, Issue 1
Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations

Yanming Lai, Kewei Liang, Ping Lin, Xiliang Lu & Qimeng Quan

Ann. Appl. Math., 40 (2024), pp. 43-70.

Published online: 2024-02

Export citation
  • 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.

  • AMS Subject Headings

65M60, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAM-40-43, author = {Lai , YanmingLiang , KeweiLin , PingLu , Xiliang and Quan , Qimeng}, title = {Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations}, journal = {Annals of Applied Mathematics}, year = {2024}, volume = {40}, number = {1}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2023-0016}, url = {http://global-sci.org/intro/article_detail/aam/22927.html} }
TY - JOUR T1 - Error Analysis of the Nonconforming $P_1$ 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 JO - Annals of Applied Mathematics VL - 1 SP - 43 EP - 70 PY - 2024 DA - 2024/02 SN - 40 DO - http://doi.org/10.4208/aam.OA-2023-0016 UR - https://global-sci.org/intro/article_detail/aam/22927.html KW - Navier-Stokes equations, error estimates, finite element method, stabilization method. AB -

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.

Lai , YanmingLiang , KeweiLin , PingLu , Xiliang and Quan , Qimeng. (2024). Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations. Annals of Applied Mathematics. 40 (1). 43-70. doi:10.4208/aam.OA-2023-0016
Copy to clipboard
The citation has been copied to your clipboard