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

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.