SINGULAR FUNCTION-METHOD FOR BOUNDARY-VAL UE-PROBLEMS WITH EDGE SINGULARITIES

The solution of an elliptic or parabolic boundary value problem on a p olyhedral cylinder is decomposable into a regular part and infinitely many (along the edges) complex singular functions. This leads to a sem i-discrete finite element method which is a priori difficult as the no n finite-dimensional space spanned by all these singular functions is incorporated into the test and trial space. By partial Fourier transfo rm in the edge directions, we show the existence of a unique discrete solution which converges optimally to the exact solution. For the para bolic equation, we also specify the requested regularity for asymptoti c error estimates in pointwise convergence.