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Finite volume method based on stabilized finite elements for the nonstationary Navier-Stokes problem. (English) Zbl 1127.76036
Summary: We investigate a finite volume method based on stabilized finite element for two-dimensional nonstationary Navier-Stokes equations. As in stabilized finite element method, macroelement condition is introduced for constructing the local stabilized formulation of nonstationary Navier-Stokes equations. Moreover, for P 1 -P 0 element, the H 1 error estimate of optimal order for finite volume solution (u h ,p h ) is analyzed. And, a uniform H 1 error estimate of optimal order for finite volume solution (u h ,p h ) is also obtained if the uniqueness condition is satisfied.
MSC:
76M12Finite volume methods (fluid mechanics)
76M10Finite element methods (fluid mechanics)
76D05Navier-Stokes equations (fluid dynamics)
65M15Error bounds (IVP of PDE)