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Datum Zeit Ort Vortrag
23.04.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 TBA
Sebastian Schöps, Technische Universität Darmstadt
16.04.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 TBA
Joscha Fregin
27.02.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 TBA
Julio Urizarna

TBA
20.02.20 13:15 Raum H - SBC5 - H0.03 Novel Space-Time Finite Element Discretizations*
Prof. Dr. Marek Behr, Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University

Moving-boundary flow simulations are an important design and analysis tool in many areas, including civil and biomedical engineering, as well as production engineering. Interface-capturing offers flexibility for complex free-surface motion, while interface-tracking is very attractive due to its mass conservation properties at low resolution. We focus on these alternatives in the context of flow simulations based on stabilized finite element discretizations of Navier-Stokes equations, including space-time formulations that allow extra flexibility concerning grid design at the interface.

Space-time approaches offer some not-yet-fully-exploited advantages; among them, the potential to allow some degree of unstructured space-time meshing. A method for generating simplex space-time meshes has been developed, allowing arbitrary temporal refinement in selected portions of space-time slabs. The method increases the flexibility of space-time discretizations, even in the absence of dedicated space-time mesh generation tools. The resulting tetrahedral and pentatope meshes are being used in the context of cavity filling flow simulations, such as those necessary to design injection molding processes.
19.02.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Comparison of Unsupervised Dimensionality Reduction Techniques (Bachelorarbeit)
Lior Polak
11.02.20 14:00 Am Schwarzenberg-Campus 5 (H), Raum H0.02 Solving nonlinear non-autonomous equations
Hendrik Vogt, Fachbereich 3 - Mathematik, Universität Bremen, Postfach 330 440, Bibliothekstraße 5, 28359 Bremen

We show the existence of solutions of nonlinear non-autonomous Cauchy problems
\[
\partial_t u(t,x) - \nabla_x \cdot (a(t,x)\nabla_xu(t,x))= f(t,x,u(t,x),\nabla u(t,x)),
\qquad u(0,\cdot)=u_0
\]
for a bounded open set $\Omega\subseteq \mathbb R^n$.
The coefficient matrix $a$ is supposed to be symmetric, uniformly elliptic,
Lipschitz continuous w.r.t.\ $t\in(0,\tau)$ and measurable w.r.t.\ $x\in\Omega$;
the nonlinearity $f$ is required to satisfy a linear growth condition.
We show that, given $u_0\in H_0^1(\Omega)$, there exists $u\in L_2(0,\tau;H_0^1(\Omega))
\cap H^1(0,\tau;L_2(\Omega))$ solving the problem mentioned above.

The proof relies on Schaefer's fixed point theorem. In the
course of the proof one uses maximal regularity properties of solutions of
inhomogeneous linear problems and compact embeddings of vector-valued Sobolev spaces.

The result partly generalises [ArCh10].

The talk is based on joint work with Wolfgang Arendt and Jürgen Voigt.


[ArCh10] W. Arendt, R. Chill: Global existence for quasilinear
diffusion equations in isotropic nondivergence form. Ann. Sc. Norm. Super. Pisa
Cl. Sci. (5) IX, 523-539 (2010).
10.02.20 10:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Das Verhalten von IDR-Verfahren unter Einfluss von Rundungsfehlern (Bachelorarbeit)
Henning Schwarz
30.01.20 14:00 Raum H - SBC5 - H0.04 Fractional derivatives and integrals as application of different functional calculi
Jan Meichsner, Institut für Mathematik (E-10), Lehrstuhl Angewandte Analysis

The question of possible generalisations of the operation of differentiation towards fractional powers can be traced back to a letter from L'Hospital to Leibniz in 1695 ([1]).
Since this time, mathematicians developed plenty of different approaches to fractional differentiation and integration generalising different aspects of the known theory.
The possibly most prominent examples are the fractional derivatives (and integrals) of Riemann-Liouville and Weyl ([4]).
Both can also be understood as instances of the sectorial functional calculus of sectorial operators as it was introduced in [2] and further promoted in [3].
Nonetheless, a direct use of the abstract techniques from operator theory seems to be rare in applications.
Therefore, the talk aims for introducing the audience in the basic principles of functional calculus and how to use it to recover the above mentioned instances of fractional derivatives.


$\mathbf{References}$

[1] B. Ross. The Development of Fractional Calculus 1695--1900. $\mathit{\text{Historia Math., 4(1):}}$ 75--89, 1977.

[2] A. McIntosh. Operators which have an $H_{\infty}$ functional calculus. $\mathit{\text{Miniconference on operator theory and partial differential equations:}}$ 210--231, 1986.

[3] M. Haase. $\mathit{\text{The Functional Calculus for Sectorial Operators,}}$ volume 169 of $\mathit{\text{Operator Theory: Advances and Applications.}}$ Birkhäuser Basel, 2006.

[4] K. S. Miller and B. Ross. $\mathit{\text{An Introduction to the Fractional Calculus and Fractional Differential Equations.}}$ John Wiley & Sons, 1993.
23.01.20 14:45 Eißendorfer Straße 40 (N), Raum 0007 Einblicke in die Modellierung des Materialverhaltens von Elastomerwerkstoffen
Nils Hendrik Kröger, Deutsches Institut für Kautschuktechnologie e.V., Hannover, Eupener Straße 33, 30519 Hannover, Deutschland

Im Maschinen- und Automobilbau werden für mechanisch extrem beanspruchte, temperatur- und chemikalienbeständige Bauteile Elastomerwerkstoffe benötigt. Typische Beispiele sind Reifen, Zahn- und Keilriemen, Motor- und Aggregatelager, Luftfedern und Fahrwerkbuchsen sowie statisch und dynamisch beanspruchte Dichtungen. Die Anforderungen bezüglich Zuverlässigkeit und Leistungsdichte sind speziell in Verbindung mit den hochsensiblen, sicherheitsrelevanten Funktionen der Bauteile besonders hoch.
Insbesondere im Rahmen der Digitalisierung in der Produktion gewinnen Simulationsmodelle verstärkt an Bedeutung. Viele Verarbeitungsschritte in der Herstellung von Elastomerbauteilen beginnend mit dem Mischen, dem Walzen und der Extrusion oder des Spritzgießens, über die Vulkanisation beeinflussen die endgültigen mechanischen Eigenschaften. Im Laufe ihres Einsatzlebens verändern sich diese Eigenschaften auf Grund von thermo-oxidativer Alterung, so dass auch Lebensdauervorhersagen zur einer Herausforderung werden. Die zuverlässige Erstellung von „Digitalen Zwillingen“ für Elastomerbauteile bedarf so einer Beschreibung vieler auch untereinander gekoppelter Effekte.
Dieser Vortrag bietet Einblicke in verschiedene Modellierungsansätze einzelner Abschnitte des Leben von Elastomeren. Hauptfokus ist hierbei die Beschreibung der mechanischen Eigenschaften unter Berücksichtigung der Vernetzung und Alterung.

Language of the talk is going to be either German or English depending on the audience preferences.
\[
\mathbf{\text{Edit: There seems to be a problem with Nils' train. The start of the talk will be delayed by 30minutes. }}
\]
16.01.20 14:00 Am Schwarzenberg-Campus 3 (E), Raum 3.074 Greedy methods in kernel based approximation
Kristof Albrecht

Positive Kernels provide methods to solve multivariate interpolation problems, but standard kernel methods usually lead to ill-conditioned linear systems. Therefore, a suitable choice of interpolation centers and basis functions reqiures particular care.

In this talk, i will give an introduction to kernel based approximation and discuss greedy point selection strategies, which will improve the stability of the interpolation method.

* Vortrag im Rahmen des Kolloquiums für Angewandte Mathematik