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Zbl 0904.76040
Boukir, K.; Maday, Y.; Métivet, B.; Razafindrakoto, E.
A high-order characteristics/finite element method for the incompressible Navier-Stokes equations. (English)
[J] Int. J. Numer. Methods Fluids 25, No.12, 1421-1454 (1997). ISSN 0271-2091; ISSN 1097-0363/e

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 2000:: *76M10 Finite element methods
76D05 Navier-Stokes equations (fluid dynamics)
65M25 Method of characteristics (numerical)

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

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Zentralblatt MATH Berlin [Germany]