Sharp-interface limit for the Navier-Stokes-Korteweg equations
Dienstag, 25.10.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Boundary and interior vortices in thin film micromagnetics
Dienstag, 8.11.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Ferromagnetic materials are described by a nonlocal and nonconvex variational principle. For certain regimes, it is possible to rigorously derive simplified models using Gamma-convergence. In my talk I will concentrate on models that contain point defects carrying a topological charge, and will discuss static and dynamical results for these defects as well as some of the underlying analytical tools.\n
Analytische und numerische Betrachtung lokaler und nicht-lokaler Phasenfeldmodelle
Dienstag, 29.11.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The elastic trefoil is the twice covered circle (joint work with Heiko von der Mosel and Henryk Gerlach)
Montag, 5.12.16, 16:15-17:15, Raum 226, Hermann-Herder-Str. 10
Mixed adaptive finite element approximation of linear elliptic equations in nondivergence form with Cordes coefficients
Dienstag, 6.12.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
This talk discusses formulations of second-order elliptic partial\ndifferential equations in nondivergence form on convex domains\nas equivalent variational problems. These formulations enable\nthe use of standard finite element techniques for variational problems\nin subspaces of \(H^2\) as well as mixed finite element methods\nfrom the context of fluid computations.\nBesides the immediate quasi-optimal a priori error bounds,\nthe variational setting allows for a posteriori error control with\nexplicit constants and adaptive mesh-refinement. The convergence of an\nadaptive algorithm is proved. Numerical results on uniform and\nadaptive meshes are included.
Active-Set-Strategien für Optimalen Transport
Dienstag, 13.12.16, 15:15-16:15, Raum 226, Hermann-Herder-Str. 10
Ein Ansatz zum Lösen von Transportproblemen ist die Approximation durch endlichdimensionale lineare Optimierungsprobleme. Diese können aber mit angemessenem Rechenaufwand nicht direkt gelöst werden.\n\nUnter gewissen Voraussetzungen sind die diskreten Lösungsmatrizen allerdings dünnbesetzt, sodass die Problemgröße durch ein Active-Set-Verfahren erheblich reduziert werden kann. \n\nIn meinem Vortrag stelle ich zwei solche Verfahren vor. Dabei wird einmal der Träger der optimalen Lösung durch die Lösung auf einem gröberen Gitter approximiert. Das zweite Verfahren verwendet die Optimalitätsbedingungen für lineare Programme, um den Träger zu approximieren.
Multi-porosity elasticity: stability and uniqueness questions
Dienstag, 20.12.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We review development of models for linear elasticity with double or triple porosity. For example, in a double porosity material there are the usual macro pores, but also the skeleton may have cracks or fissures which are known as micro pores. Such materials have a multitude of applications in today's world, including to the controversial subject of hydraulic fracturing for gas ("fracking").\n\nWe look at the question of establishing a uniqueness theorem when the elastic coefficients are only symmetric and not required to be sign definite. The extension to stability under the same conditions is analysed. If time permits we shall also look at the extension of the linear theory to the fully nonlinear one and discuss aspects of nonlinear wave propagation.
Boundary triples, Krein formula, and resolvent estimates for one-dimensional high-contrast periodic problems
Dienstag, 21.2.17, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10