Numerische Simulation Auf Massiv Parallelen Rechnern Crouzeix-raviart Type Nite Elements on Anisotropic Meshes

The paper deals with a non-conforming nite element method on a class of anisotropic meshes. The Crouzeix-Raviart element is used on triangles and tetrahedra. For rectangles and prismatic (pentahedral) elements a novel set of trial functions is proposed. Anisotropic local interpolation error estimates are derived for all these types of element and for functions from classical and weighted Sobolev spaces. The consistency error is estimated for a general diierential equation under weak regularity assumptions. As a particular application, an example is investigated where anisotropic nite element meshes are appropriate, namely the Poisson problem in domains with edges. A numerical test is described.