A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem (Advances in Applied Mathematics and Mechanics, 2012)
We construct a finite volume element method based on the constrainednonconforming rotated Q1-constant element (CNRQ1-P0) for the Stokes problem.Two meshes are needed, which are the primal mesh and the dual mesh. We approximatethe velocity by CNRQ1 elements and the pressure by piecewise constants.The errors for the velocity in the H1 norm and for the pressure in the L2 norm areO(h) and the error for the velocity in the L2 norm is O(h2). Numerical experimentsare presented to support our theoretical results.