An efficient finite element method for treating singularities in Laplace's equation (Q811101)

The paper deals with two plane boundary value problems for the Laplace equation (the Motz problem and the cracked-beam problem) involving discontinuities in boundary conditions. The proposed methods depend on seeking the approximate solution in the form \(u=\sum^{N}_{i=1}u_ i\Phi^ i+\sum^{M}_{i=1}\alpha_ iW^ i\) where \(\Phi^ i\) are basis functions connected with the ordinary finite element method and \(W^ i\) denote the suitably defined singular basis functions. A number of results of numerical experiments is given.