Bulletin of the
Korean Mathematical Society BKMS

In this article, we propose and analyze a new nonconforming primal mixed finite element method for the stationary Stokes equations. The approximation is based on the pseudostress-velocity formulation. The incompressibility condition is used to eliminate the pressure variable in terms of trace-free pseudostress. The pressure is then computed from a simple post-processing technique. Unique solvability and optimal convergence are proved. Numerical examples are given to illustrate the performance of the method.

Keywords: primal mixed finite elements, nonconforming methods, error estimates, Stokes problems, pseudostress-velocity formulation

MSC numbers: Primary 58B34, 58J42, 81T75