This paper reviews the state of the art and discusses very recent mathematical
developments in the field of adaptive boundary element methods. This includes an overview …

We present a high-order boundary integral equation solver for 3D elliptic boundary value
problems on domains with smooth boundaries. We use Nyström's method for discretization …

Averaging techniques for finite element error control, occasionally called ZZ estimators for
the gradient recovery, enjoy a high popularity in engineering because of their striking …

In this paper we propose and analyze a hybrid hp boundary element method for the solution
of problems of high frequency acoustic scattering by sound-soft convex polygons, in which …

We solve first-kind Fredholm boundary integral equations arising from Helmholtz and
Laplace problems on bounded, smooth screens in three dimensions with either Dirichlet or …

We consider the variational formulation of the electric field integral equation on bounded
polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based …

We study a multilevel preconditioner for the Galerkin boundary element matrix arising from a
symmetric positive-definite bilinear form. The associated energy norm is assumed to be …

We study a preconditioner for the h‐p version of the boundary element method for
hypersingular integral equations in three dimensions. The preconditioner is based on a …

Several textbooks and monographs on preconditioners for FEM (finite element methods) are
available, but none exists for BEM (boundary element methods). For BEM, the topic is dealt …

We prove an a priori error estimate for the hp-version of the boundary element method with
hypersingular operators on piecewise plane open or closed surfaces. The underlying …