Numerical analysis of a characteristic stabilized finite element method for the time-dependent Navier-Stokes equations with nonlinear slip boundary conditions. (English) Zbl 1415.76455
Summary: Based on a characteristic method, this work is concerned with a finite element approximation to the time-dependent Navier-Stokes equations with nonlinear slip boundary conditions. Since this slip boundary condition of friction type contains a subdifferential property, its continuous variational problem is formulated as an inequality, which can turn into an equality problem by using a powerful regularized method. Then a fully discrete characteristic scheme under the stabilized lower order finite element pairs is proposed for the equality problem. Optimal error estimates for velocity and pressure are derived under the corresponding \(L^2, H^1\)-norms. Finally, a smooth problem test is reported to demonstrate the theoretically predicted convergence order and the expected slip phenomena, and the simulation of a bifurcated blood flow model is displayed to illustrate the efficiency of the proposed method.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
Keywords:
time-dependent Navier-Stokes equations; nonlinear slip boundary conditions; characteristic method; lower order finite element pairs; error estimatesReferences:
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