SINGULAR FUNCTION-METHOD FOR BOUNDARY-VALUE-PROBLEMS WITH EDGE SINGULARITIES

The solution of an elliptic or parabolic boundary value problem on a polyhedral cylinder is decomposable into a regular part and infinitely many (along the edges) complex singular functions. This leads to a semi-discrete finite element method which is a priori difficult as the non finite-dimensional space spanned by all these singular functions is incorporated into the test and trial space. By partial Fourier transform in the edge directions, we show the existence of a unique discrete solution which converges optimally to the exact solution. For the parabolic equation, we also specify the requested regularity for asymptotic error estimates in pointwise convergence.