Semi-discrete Galerkin approximations for the single-layer equation on Lipschitz curves (Q1386648)

This paper provides a stability and error analysis for a class of Galerkin methods for the single-layer equation on piecewise-smooth curves in the plane. These Galerkin methods use piecewise-constant basis functions, but the mesh on the boundary curve need not be uniform. The only requirement is that the quadrature method used to approximate the Galerkin integrals be sufficiently exact, either by the choice of a fine enough grid or by the use of a proper quadrature order.