Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, part I: weakly-singular integral equation

Abstract

We analyze an adaptive boundary element method for Symm's integral equation in 2D and 3D which incorporates the approximation of the Dirichlet data $$g$$ g into the adaptive scheme. We prove quasi-optimal convergence rates for any $$H^{1/2}$$ H 1 / 2 -stable projection used for data approximation.