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 …

For the simple layer potential V associated with the three-dimensional (3D) Laplacian, we
consider the weakly singular integral equation Vϕ=f. This equation is discretized by the …

We prove convergence and quasi-optimality of a lowest-order adaptive boundary element
method for a weakly-singular integral equation in 2D. The adaptive mesh-refinement is …

This paper presents adaptive boundary element methods for positive, negative, as well as
zero order operator equations, together with proofs that they converge at certain rates. The …

A posteriori error estimation and related adaptive mesh-refining algorithms have themselves
proven to be powerful tools in nowadays scientific computing. Contrary to adaptive finite …

Abstract The hh/2-strategy is one well-known technique for the a posteriori error estimation
for Galerkin discretizations of energy minimization problems. One considers η:= ‖ h/2 …

A variational inequality (VI) and a mixed formulation for an elliptic obstacle problem are
considered. Both formulations are discretized by an hp-FE interior penalty discontinuous …

We consider the solution of a second order elliptic PDE with inhomogeneous Dirichlet data
by means of adaptive lowest-order FEM. As is usually done in practice, the given Dirichlet …

We report on the Matlab program package HILBERT. It provides an easily-accessible
implementation of lowest order adaptive Galerkin boundary element methods for the …

A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary
element computations. For hypersingular integral equations in 2D with a positive-order …