We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair （piecewise bilinear veloc- ities and pressures） and piecewise c...We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair （piecewise bilinear veloc- ities and pressures） and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the H1 norm and the pressure in the L2 norm. In addition, a second order optimal error estimate for the velocity in the L2 norm is derived. Numerical experiments illustrating the theoretical results are included.展开更多
文摘We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair （piecewise bilinear veloc- ities and pressures） and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the H1 norm and the pressure in the L2 norm. In addition, a second order optimal error estimate for the velocity in the L2 norm is derived. Numerical experiments illustrating the theoretical results are included.
