Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces

Boundary approximation techniques are described for solving homogeneous self-adjoint elliptic equations. Piecewise expansions into particular solutions are used which approximate both the boundary and interface conditions in a least squares sense. Convergence of such approximations is proved and error estimates are derived in a natural norm. Numerical experiments are reported for the singular Motz problem which yield extremely accurate solutions with only a modest computational effort.