Penalty-Factor-Free Discontinuous Galerkin Methods for 2-Dim Stokes Problems

This paper presents two new finite element methods for two-dimensional Stokes problems. These methods are developed by relaxing the constraints of the Crouzeix–Raviart nonconforming P1 finite elements. Penalty terms are introduced to compensate for lack of continuity or the divergence-free property. However, there is no need for choosing penalty factors, and the formulations are symmetric. These new methods are easy to implement and avoid solving saddle-point linear systems. Numerical experiments are presented to illustrate the proved optimal error estimates.