A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges

The solution of the Stokes problem in three-dimensional domains with edges has anisotropic singular behaviour which is treated numerically by using an isotropic finite element meshes. The velocity is approximated by Crouzeix-R aviart (nonconforming P-1 ) elements and the pressure by piecewise constant s. This method is stable for general meshes (without minimal or maximal ang le condition). Denoting by N-e the number of elements in the mesh, the inte rpolation and consistency errors are of the optimal order h similar to N-e( -1/3) which is proved for tensor product meshes. As a by-product, we analys e also nonconforming prismatic elements with P-1 + span {x(3)(2)} as the lo cal space for the velocity where x(3) is the direction of the edge.