This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …

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 …

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 …

For hypersingular integral equations in 2D and 3D, we analyze easy-to-implement error
estimators like (h− h/2)-based estimators, two-level estimators, and averaging on large …

For some Poisson-type model problem, we prove that adaptive FEM driven by the (h− h∕ 2)-
type error estimators from Ferraz-Leite et al.(2010) leads to convergence with optimal …

We discuss several adaptive mesh-refinement strategies based on (h− h/2)-error estimation.
This class of adaptive methods is particularly popular in practise since it is problem …

Since the advent of isogeometric analysis (IGA) in 2005, the finite element method (FEM)
and the boundary element method (BEM) with splines have become an active field of …

A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary
element computations. We analyze the mathematical relation between the hh/2-error …