Local convergence of the boundary element method on polyhedral domains

The local behavior of the lowest order boundary element method on quasi-uniform meshes for Symm’s integral equation and the stabilized hyper-singular integral equation on polygonal/polyhedral Lipschitz domains is analyzed. We prove local a priori estimates in [Formula: see text] for Symm’s integral equation and in [Formula: see text] for the hyper-singular equation. The local rate of convergence is limited by the local regularity of the sought solution and the sum of the rates given by the global regularity and additional regularity provided by the shift theorem for a dual problem.