A Stabilized Characteristic-Nonconforming Finite Element Method for Time-Dependent Incompressible Navier–Stokes Equations

Abstract

In this paper, we study a stabilized characteristic-nonconforming finite element method to solve the time-dependent incompressible Navier–Stokes equations. The characteristic scheme is used to deal with advection term and temporal differentiation, which avoid some difficulties caused by trilinear terms. The space discretization utilizes the nonconforming lowest equal-order pair of mixed finite elements (i.e. \(\textit{NCP}_1-{\mathbf {P}}_1\)). The stability analysis and optimal-order error estimates for velocity and pressure are presented. Numerical results are also provided to verify theory analysis.