MESH REFINEMENT AND WINDOWING NEAR EDGES FOR SOME ELLIPTIC PROBLEM

The solutions of elliptic problems in three-dimensional domains with edges contain singularities, in general, which influence the order of convergence of the standard finite element, method. In this paper, for some elliptic problem with a special, but typical edge singularity function, an appropriate local mesh refinement is studied. Estimates of the rate of convergence with respect to the L2- and W1,2-norm are proved and, moreover, bounds of the condition number of the matrix associated with this approximation are derived. By means of some error estimates for subdomains, the justification of a two-step finite element discretization (windowing-technique) is given.