Asymptotic and A posteriori error estimates for boundary element solutions of hypersingular integral equations

This paper is devoted to the analysis of the numerical solution of the exterior Neumann problem for the Helmholtz equation formulated as a hypersingular integral equation. Three boundary element Galerkin methods for the solution of the screen problem are investigated when the boundary is an open surface (screen): standard h-version, augmented A-version, and h-p version. Their convergence is proven and a detailed discussion of a posteriori error estimates based on the residual error method is presented. An adaptive boundary element algorithm based on the estimates is also presented.