Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian

We generalize the a posteriori techniques for the linear heat equation in [Ver03] to the case of the nonlinear parabolic p-Laplace problem thereby proving reliable and efficient a posteriori error estimates for a fully discrete implicite Euler Galerkin finite element scheme. The error is analyzed using the so-called quasi-norm and a related dual error expression. This leads to equivalence of the error and the residual, which is the key property for proving the error bounds

Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes problems

We extend the ideas of Diening, Kreuzer, and Stevenson [Instance optimality of the adaptive maximum strategy, Found. Comput. Math. (2015)], from conforming approximations of the Poisson problem to nonconforming Crouzeix-Raviart approximations of the Poisson and the Stokes problem in 2D. As a consequence, we obtain instance optimality of an AFEM with a modified maximum marking strategy

Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology

We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are related by a, possibly multi–valued, maximal monotone $r$-graph, with $1 < r < \infty$. Using a variety of weak compactness techniques, including Chacon’s biting lemma and Young measures, we show that a subsequence of the sequence of finite element solutions converges to a weak solution of the problem as the finite element discretization parameter $h$ tends to 0. A key new technical tool in our analysis is a finite element counterpart of the Acerbi–Fusco Lipschitz truncation of Sobolev functions

Convergence of adaptive finite element methods with error-dominated oscillation

Recently, we devised an approach to a posteriori error analysis, which clarifies the role of oscillation and where oscillation is bounded in terms of the current approximation error. Basing upon this approach, we derive plain convergence of adaptive linear finite elements approximating the Poisson problem. The result covers arbritray H^-1-data and characterizes convergent marking strategies

"Deutschland kann nur durch Deutschland gerettet werden": der Kampf um das nationale Erbe der Befreiungskriege am Berliner Dönhoffplatz im 19. und 20. Jahrhundert

The former Dönhoffplatz has been renamed the Marion-Gräfin-Dönhoff-Platz in 2010. The University of Nottingham provided the historical background research on the history of the Platz which dates back to the 1740s. The findings are presented in this Preprint version and add to the information on the memorial plate on the Platz. The article's main focus is on the history of the monuments of the two Prussian reformers Freiherr vom Stein and Fürst Hardenberg which were errected on the Dönhoffplatz. The Platz and the two monuments symbolize the underresearched "civil" legacy of the wars of liberation in the Prussian-German capital, which caused heated debates in the 19th and in the 20th century. So far, historians have mainly focused on the history of the Brandenburg Gate and the military legacy enshrined in the Neue Wache Unter den Linden. This is the first time that the largely forgotten history of the "civil" monuments on the Doenhoffplatz is analysed

On the threshold condition for Dörfler marking

It is an open question if the threshold condition θ θ_* the algebraic converges rate can be made arbitrarily small