An Analysis of Penalty-Nonconforming Finite Element Method for Stokes Equations

In this paper, the penalty-nonconforming finite element method for Stokes equations is considered. An abstract error estimate is given. For Crouzeix-Raviart nonconforming triangular elements, in particular, the analysis shows that the "reduced integration" technique is not necessary in the integration of the penalty term on each element. It means that a loss of precision is avoided in this penalty method.