A high-order characteristics/finite element method for the incompressible Navier-Stokes equations. (English) Zbl 0904.76040

Boukir, K.; Maday, Y.; Métivet, B.; Razafindrakoto, E.

Int. J. Numer. Methods Fluids 25, No. 12, 1421-1454 (1997).

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.

MSC:

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

Keywords:

second-order time scheme; characteristics method; stability; optimal error estimates; Courant-Friedrichs-Levy condition; code N3S

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