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

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g$$\end{document} into the adaptive scheme. We prove quasi-optimal convergence rates for any H1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{1/2}$$\end{document}-stable projection used for data approximation.