Numerische Simulation Auf Massiv Parallelen Rechnern Preprint-reihe Des Chemnitzer Sfb 393

The nite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges Abstract. This paper is concerned with a speciic nite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the nite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates for functions from anisotropically weighted spaces are derived. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.