This paper aims first at a simultaneous axiomatic presentation of the proof of optimal
convergence rates for adaptive finite element methods and second at some refinements of …

We review different techniques to enforce essential boundary conditions, such as the
(nonhomogeneous) Dirichlet boundary condition, within a discrete variational framework …

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 …

Newest vertex bisection (NVB) is a popular local mesh-refinement strategy for regular
triangulations that consist of simplices. For the 2D case, we prove that the mesh-closure step …

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations
of certain nonlinear second-order partial differential equations. We allow continuous …

We provide an abstract framework for optimal goal-oriented adaptivity for finite element
methods and boundary element methods in the spirit of [C. Carstensen et al., Comput. Math …

We prove that for compactly perturbed elliptic problems, where the corresponding bilinear
form satisfies a Gårding inequality, adaptive mesh-refinement is capable of overcoming the …

Given an arbitrary function in, we show that the error attained by the global-best
approximation by-conforming piecewise polynomial Raviart–Thomas–Nédélec elements …

The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to
compute an approximation of user-prescribed accuracy at quasi-minimal computation time …

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 …