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

• DOI: 10.1007/s10092-013-0100-x
• Publication Date: 2013-10-18T13:12:46Z
• Authors: Michael Feischl; Thomas Führer; Michael Karkulik; Jens Markus Melenk; Dirk Praetorius
• Keywords: Theory of computation

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.