We propose a continuous interior penalty (CIP) method for the pure transport problem and for the viscosity dependent 'Stokes-Brinkman' problem where the gradient jump penalty is localized to faces in the interior of subdomains. Special focus is given to the case, where the subdomains are so-called composite finite elements, i.e., for instance, quadrilateral, hexahedral or prismatic elements which are composed by simplices such that the arising global simplicial mesh is regular.
The big advantage of this local CIP is that it allows for static condensation in contrast to the classical CIP method. If the degrees of freedom in the interior of the composite finite elements are eliminated using static condensation then the resulting couplings of the skeleton degrees of freedom are comparable to those for classical conforming finite element methods which leads to a substantially smaller matrix stencil than for the standard global CIP-method. Optimal stability and error estimates are proved and numerical tests are presented.
For the Stokes-Brinkman model, our error bound does not increase if the viscosity parameter tends to zero which is mainly caused by adding a penalty term for the divergence of the velocity in the discretization. Moreover, the reduction effect of the static condensation is much stronger for this model since, beside of the elimination of all velocity degrees of freedom in the interior of each composite cell, all pressure degrees of freedom except for the cell-wise constants can be eliminated.

A common problem in multi-layer shear flows, especially from the perspective of process engineering, is the occurrence of interfacial instabilities. For purely viscous fluids these occur at low Reynolds numbers. However, multi-layer duct flows can be stabilised by astute positioning of a visco-plastic fluid as the lubricant that remains unyielded at the interface. This technique has been termed visco-plastic lubrication.
In this talk, I will start with an introduction to Visco-Plastically Lubricated (VPL) flows. Then I will present the results of a systematic study aimed at extending visco-plastic lubrication from a theoretical concept towards more industrial applications. The results come in two parts. Firstly, a computational study of VPL flows will be presented in the setting of a Newtonian core fluid surrounded by a Bingham lubricating fluid, within pipe and channel configurations. Flow development and start-up are explored. Nonlinear perturbations are also studied to obtain better understanding about the stability of these flows, e.g. what role does the unyielded plug play, do perturbations remain concentric or develop asymmetries, how large an amplitude of perturbation can be withstood and at what flow rate. Theseare essential questions for industrial prototyping. Secondly, I will show the feasibility of VPL flows with viscoelastic core fluids from both experimental and theoretical perspectives. Viscoelastic fluids are frequently used in the polymer and food industries, which are large areas for application.
I will close by connecting visco-plastic lubrication to potential novel applications such as visco-plastic sculpting and large droplet encapsulation.

Eine interaktive Informationsveranstaltung für Studierende (ab dem 3. Semester) und Doktorand(inn)en der Mathematik und Wirtschaftsmathematik an der TU Dortmund, die sich in entspannter Atmosphäre einen ersten Eindruck von uns verschaffen und mehr über unsere Arbeitsweise und den Berufsalltag in der Topmanagement-Beratung erfahren wollen. Unsere Berater(innen) vor Ort, die alle selbst über einen MINT- Studienhintergrund verfügen und/oder an der TU Dortmund studiert bzw. promoviert haben, erläutern Ihnen zudem gerne, inwiefern Sie Ihr spezifisches Studienwissen in unsere Klientenarbeit einbringen können – und zeigen Ihnen auf Wunsch Ihre individuellen Einstiegs- und Entwicklungsmöglichkeiten in einem außergewöhnlich interdisziplinären und internationalen Arbeitsumfeld auf. Informieren Sie sich!

We address the exact solution of a very challenging (and previously unsolved) instance of the quadratic 3-dimensional assignment problem, arising in digital wireless communications. When error correction of a transmitted message is not possible, an automatic repeat request (ARQ) may be sent. For the case of PSK coding we describe the techniques developed to solve this instance to proven optimality, from the choice of an appropriate mixed integer programming formulation, to cutting planes and symmetry handling. Combining these approaches we are able to solve this problem with moderate computational effort (2.5 million nodes and the equivalent of one week of computations on a standard PC). This is joint work with Domenico Salvagnin, University of Padova.

Wir studieren freie Randwertprobleme, also partielle Differentialgleichungen in Gebieten mit unbekannten Rändern. Zur numerischen Behandlung solcher Probleme untersuchen wir die Phasenfeld-Methode, bei der scharfe Übergänge in einer kleinen Umgebung des Randes ``ausgeschmiert`` werden. Als konkrete Anwendung wird ein Osmose-Modell vorgestellt und numerisch untersucht, das auf Massenerhaltung und Oberflächenspannung beruht .

Wir stellen einige klassische Verfahren vor, die in der Wissenschaft vom Ver- und Entschlüsseln Verwendung finden. Jedes Kryptosystem birgt seine Schwächen. Deshalb besteht eine Hälfte des Vortrags aus verschiedenen Attacken auf diese Systeme. Alle Verfahren werden anhand konkreter Beispiele behandelt. Der Vortrag eignet sich besonders für Studentinnen und Studenten und ist zum großen Teil auch für interessierte Nicht-Mathematiker/-innen verständlich.

A reconfiguration problem is the reachability problem on an interesting class of graphs, namely the solution graphs of a combinatorial problem: Given two solutions to some instance, the task is to decide whether one solution can be transformed into the other via ``local'' changes while maintaining feasibility. For example, given two k-colorings of a graph, the task is to decide whether one can be transformed into the other by changing the color of a single vertex at a time, such that each intermediate coloring is proper. It turns out that the complexity of reconfiguration problems bears some surprises in the sense that a reconfiguration problem can be hard although its underlying combinatorial problem is tractable and vice versa. We give an overview of some recent results and techniques in this area, with a focus on vertex coloring and matchings (and their relation to sliding token puzzles).

In this talk we present a review and some extensions on how indicator constraints in Mixed Integer Programming (MIP) are handled. In particular, we explore the disjunctive programming paradigm in this context, opposed to the classical big-M method. In the case of Mixed Integer Linear Programming, a clear relation between the two can be derived. We present some computational results that suggest the use of local information in MIP with Indicator constraints and sketch some ideas in this direction.

The software IPO is presented which investigates a polyhedron P given by means of an optimization oracle, e.g., a mixed-integer hull and a MIP solver. It detects all equations, can check adjacency of vertices, and compute some facets valid for P in exact arithmetic. The facets are produced in such a way that they are helpful in optimizing a given objective function, using target cuts introduced by Buchheim, Liers, and Oswald in 2008. In contrast to usual convex-hull algorithms which produce the entire description, but run out of resources for small dimensions already, IPO can handle much larger dimensions. www.math.uni-magdeburg.de/institute/imo/ag_kaibel/software/IPO/

Nicht zuletzt durch die Finanzkrisen ist die Bedeutung von Modellrisiken für das Risikomanagement auf Finanz- und Energiemärkten in das öffentliche Bewusstsein gerückt. Wir klären die grundlegenden Begriffe ``Risiko, Unsicherheit und Ambiguität`` zur Analyse von Modellrisiken und stellen anschließend verschiedene Ansätze zur Quantifizierung von Modellrisiken vor. Mittels verschiedener Beispiele illustrieren wir Varianten von Modellrisiken.

In this talk, I will consider mixed-integer convex minimization problems. First, I will present optimality conditions for this class of optimization problems. Then, I will introduce the concept of center-points, a generalization of the median from the one dimensional space to vector spaces. Through the theory of center-points I will show how to extend the general cutting plane scheme from the continuous setting to the mixed-integer setting. Further, I will present several properties of center-points and how to compute them approximately.