The two-grid stabilization of equal-order finite elements for the stokes equations

This work presents a two-grid stabilized method of equal-order finite elements for the Stokes problems. This method only offsets the discrete pressure space by the residual of pressure on two grids to circumvent the discrete Babuška-Brezzi condition. The method can be done locally in a two-grid approach without stabilization parameter by projecting the pressure onto a finite element space based on coarse mesh. Also, it leads to a linear system with minimal additional cost in implement. Optimal error estimates are obtained. Finally, some numerical simulations are presented to show stability and accuracy properties of the method.