On the finite element method for a singular problem (Q1194412)

The paper is concerned with a finite element method for a boundary value problem with Laplace's equation on a slotted rectangle. In order to cover the singularity of the exact solution, an expansion into a series of `` singular functions'' (with increasing degree of smoothness) is used to obtain a suitable set of basis functions for a finite element method with triangular elements: It consists of the ``usual'' piecewise linear functions and some of the singular functions. It is shown that the method converges linearly. A numerical example indicates that two singular functions in the basis are enough.