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A stabilized characteristic-nonconforming finite element method for time-dependent incompressible Navier-Stokes equations. (English) Zbl 1383.35140

Summary: 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., \(NCP_1-\mathbf P_1\)). The stability analysis and optimal-order error estimates for velocity and pressure are presented. Numerical results are also provided to verify theory analysis.

MSC:

35Q30 Navier-Stokes equations
76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
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