A nonconforming-conforming finite element method for solving 3D Stokes problems

Abstract:

In this paper, we study nonconforming finite element methods for 3D Stokes problems. We use nonconforming rotated $Q_1$ elements for the approximation of the first two components of the velocity, the conforming trilinear element for the approximation of the third component and piecewise constant for the approximation of pressure. Optimal error estimates are derived, which are both first order for H1-seminorm of velocity $\textbf{u}$ and $L^2$ norm of pressure $p$. Numerical experiments are provided to verify the theoretical results.