@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} }