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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 and Qimeng Quan

Ann. Appl. Math. DOI: 10.4208/aam.OA-2023-0016

Publication Date : 2023-09-04

  • 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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