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A high-order characteristics/finite element method for the incompressible Navier-Stokes equations. (English) Zbl 0904.76040
Summary: We consider a discretization of the incompressible Navier-Stokes equations involving a second-order time scheme based on the characteristics method and a spatial discretization of finite element type. Theoretical and numerical analyses are detailed and we obtain stability results and optimal error estimates on the velocity and pressure under a time step restriction less stringent than the standard Courant-Friedrichs-Levy condition. Finally, some numerical results obtained with the code N3S are shown which justify the interest of this scheme and its advantages with respect to an analogous first-order time scheme.

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
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