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A new mixed finite element formulation and the MAC method for the Stokes equations. (English) Zbl 0918.76036
A mixed finite element scheme is constructed for Stokes equations, in which two components of velocity and the pressure are determined on different meshes. The authors present optimal first-order error estimates for velocity and pressure, and point out a natural connection between the well-known marker and cell (MAC) method and the proposed scheme. The authors give a variational formulation of Stokes equations by using primitive variables, and then derive optimal error estimates for the MAC scheme. The above connection can serve as a bridge for extending the MAC scheme to high-order approximations and to the three-dimensional case.
MSC:
76M10Finite element methods (fluid mechanics)
76D07Stokes and related (Oseen, etc.) flows