Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods Part II. The three-dimensional case

Summary.

In this paper we introduce new local a-posteriori error indicators for the Galerkin discretization of three-dimensional boundary integral equations. These error indicators are efficient and reliable for a wide class of integral operators, in particular for operators of negative order. They are based on local norms of the computable residual and can be used for controlling the adaptive refinement. The proofs of efficiency and reliability are based on the result that the Aronszajn-Slobodeckij norm $\|\cdot\|_{H^s(\Gamma)}$ (given by a double integral for a non-integer $s\in{\mathbb R}_{>0}\setminus{\mathbb N}$) is localizable for certain functions. Neither inverse estimates nor saturation properties are needed. In this paper, we extend the two-dimensional results of a previous paper to the three-dimensional case.