Simple Error Estimators for the Galerkin BEM for some Hypersingular Integral Equation in 2D

A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. For hypersingular integral equations in 2D with positive-order Sobolev space, we analyze the mathematical relation between the h − h/2error estimator from [18], the two-level error estimator from [22], and the averaging error estimator from [7]. All of these a posteriori error estimators are simple in the following sense: First, the numerical analysis can be done within the same mathematical framework, namely localization techniques for the energy norm. Second, there is almost no implementational overhead for the realization. In particular, this is very much different to other a posteriori error estimators proposed in the literature. As model example serves the hypersingular integral equation associated with the 2D Laplacian, and numerical experiments underline the mathematical results.