Weighted Error Estimators for the Incompressible Navier-Stokes Equations

We present the application of weighted a posteriori error estimation to the incompressible Navier-Stokes equations. Using information from an appropriate dual problem, we control the discretization error of a functional of the solution as the drag or lift coefficient of an object immerged in a fluid. As test cases we consider a benchmark problem of a chanel flow and the flow around a cylinder in an unbounded domain

Democracy

Non-fiction by Roland Becke

Finite element formulation of general boundary conditions for incompressible flows

We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a discrete weighted weak formulation valid for all values of the viscosity parameter, including the limit case of the Euler equations. In order to control the discrete kinetic energy, additional consistent terms are introduced. We treat the limit case as a (degenerate) system of hyperbolic equations, using a balanced spectral decomposition of the flux Jacobian matrix, in analogy with compressible flows. Then, following the theory of Friedrich's systems, the natural characteristic boundary condition is generalized to the considered physical boundary conditions. Several numerical experiments, including standard benchmarks for viscous flows as well as inviscid flows are presented

Environment

Non-fiction by Roland W. Becke

Zur Problematik der Verbindung von Strafe und Pädagogik im Maßnahmenvollzug

Zusammenfassung: Der Beitrag problematisiert die Verbindung von Strafe und Pädagogik bzw. Therapie im Maßnahmenvollzug gemäß dem Schweizerischen Strafrecht. Anhand einer Falldarstellung zum Fall einer Jugendlichen in einem Jugendheim werden die Probleme, die sich aus der richterlich verordneten Erziehungsmaßnahme für die Jugendlichen und für das pädagogische Personal ergeben können, verdeutlicht. Anschließend an die Falldarstellung werden die Rechtsgrundlage für Maßnahmen im Schweizer Strafrecht erörtert und Strukturmerkmale von Strafe und Pädagogik bzw. Therapie gegenübergestellt und verglichen. Der Vergleich macht deutlich, dass die Verknüpfung der unterschiedlichen Handlungslogiken nicht widerspruchsfrei möglich ist und Pädagogik bzw. Therapie von der Logik der Strafe dominiert wird. Anschließend wird die Bedeutung der Freiwilligkeit in der Interventionspraxis der Sozialen Arbeit diskutiert. Abschließend werden Vorschläge für die Weiterentwicklung der Praxis skizzier

A Finite Element Method for Domain Decomposition with Non-Matching Grids

In this note we propose and analyse a new method for handling interfaces between non-matching grids based on an approach suggested by Nitsche [12] for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given, and we discuss the relation to the mortar finite element method. Some numerical results are included

2.1 Detailed brood evaluation under field conditions: advantages and disadvantages

Bee brood studies under semi-field conditions according to OECD GD 75 display a strong variability of the brood termination rates (BTRs) as the key endpoint. Therefore, the ICP-PR Bee Brood Group considered the performance of EPPO 170 field studies using the OECD GD 75 bee brood evaluation as one option to achieve more reliable BTR data. This approach was envisaged already some years ago and used for several years. However, broader data sets supporting the benefit of this combined methodology were still lacking.The analysis of current field studies performed since 2012 indicate that control BTRs were approximately half the size compared to values observed under semi-field conditions. Moreover, results give a strong indication that the BTR values under field conditions are more reliable and less variabel. Therefore, the combined method is a valuable tool to investigate potential effects of a plant protection product on the bee brood to refine the risk under realistic exposure conditions.Bee brood studies under semi-field conditions according to OECD GD 75 display a strong variability of the brood termination rates (BTRs) as the key endpoint. Therefore, the ICP-PR Bee Brood Group considered the performance of EPPO 170 field studies using the OECD GD 75 bee brood evaluation as one option to achieve more reliable BTR data. This approach was envisaged already some years ago and used for several years. However, broader data sets supporting the benefit of this combined methodology were still lacking.The analysis of current field studies performed since 2012 indicate that control BTRs were approximately half the size compared to values observed under semi-field conditions. Moreover, results give a strong indication that the BTR values under field conditions are more reliable and less variabel. Therefore, the combined method is a valuable tool to investigate potential effects of a plant protection product on the bee brood to refine the risk under realistic exposure conditions

Adaptive FEM for parameter-errors in elliptic linear-quadratic parameter estimation problems

We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. A novel a priori bound for the parameter error is proved and, based on this bound, an adaptive finite element method driven by an a posteriori error estimator is presented. Unlike prior results in the literature, our estimator, which is composed of standard energy error residual estimators for the state equation and suitable co-state problems, reflects the faster convergence of the parameter error compared to the (co)-state variables. We show optimal convergence rates of our method; in particular and unlike prior works, we prove that the estimator decreases with a rate that is the sum of the best approximation rates of the state and co-state variables. Experiments confirm that our method matches the convergence rate of the parameter error