Stable nonconforming quadrilateral finite elements for the Stokes problem

摘要

Stability result is obtained for the approximation of the stationary Stokes problem with nonconforming elements proposed by Douglas et al. [J. Douglas Jr., J.E. Santos, D.S. Xiu Ye, Nonconforming Galerkin methods based on Quadrilateral Elements for second Order Elliptic Problems, Preprints] added by conforming bubbles to the velocity and discontinuous piecewise linear to the pressure on quadrilateral elements. Optimal order error estimates derived.