A mixed convergent formulation for the three-dimensional Stokes equations

Abstract

This paper deals with the Stokes problem in a bounded domain of $\mathbb{R}^{3}$ with a polyhedral boundary. The formulation involves the vorticity and the vector potential. The method is exactly incompressible and general boundary conditions can be taken into account. The discrete problem is based on a stabilized formulation depending on a nonnegative parameter. For a suitable choice of this parameter, the method converges when using first degree Nedelec elements without any assumption on the regularity of the exact solution. Standard convergence results are improved when using higher degree Nedelec elements.