For the discretization of the integral fractional Laplacian $(-\Delta)^ s $, $0< s< 1$, based on
piecewise linear functions, we present and analyze a reliable weighted residual a posteriori …

We analyze an adaptive boundary element method for the weakly-singular and
hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed …

We present a new AFEM for the Laplace–Beltrami operator with arbitrary polynomial degree
on parametric surfaces, which are globally W^ 1_ ∞ W∞ 1 and piecewise in a suitable …

We consider an adaptive finite element method with arbitrary but fixed polynomial degree
p≥ 1, where adaptivity is driven by an edge-based residual error estimator. Based on the …

Based on the Uzawa algorithm, we consider an adaptive finite element method for the
Stokes system. We prove linear convergence with optimal algebraic rates for the residual …

For the singular integral definition of the fractional Laplacian, we consider an adaptive finite
element method steered by two-level error indicators. For this algorithm, we show linear …

The goal of this work is to generalize the analysis of adaptive algorithms for finite element
methods (FEM) and boundary element methods (BEM) from elliptic problems, satisfying the …