Numerische Simulation Auf Massiv Parallelen Rechnern a Non-conforming Nite 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 anisotropic nite element meshes. The velocity is approximated by Crouzeix-Raviart (non-conforming P 1) elements and the pressure by piecewise constants. This method is stable for general meshes (without minimal or maximal angle condition). The interpolation and consistency errors are of the optimal order h N ?1=3 which is proved for tensor product meshes. As a by-product, we analyse also non-conforming prismatic elements with P 1 span fx 2 3 g as the local space for the velocity where x 3 is the direction of the edge.