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 - <p style="text-align: justify;">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.</p>