| Popis: |
This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones. |
