The finite volume method based on stabilized finite element for the stationary Navier-Stokes problem

A finite volume method based on stabilized finite element for the two-dimensional stationary Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation for the problem. We obtain the well-posedness of the FVM based on stabilized finite element for the stationary Navier-Stokes equations. Moreover, for quadrilateral and triangular partition, the optimal H^1 error estimate of the finite volume solution u"h and L^2 error estimate for p"h are introduced. Finally, we provide a numerical example to confirm the efficiency of the FVM.

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