Events & Teaching

Upcoming Events

go to archive

Monday, 06.02.2012, 16.15 Uhr (FU Berlin): Oberseminar Nonlinear Dynamics
D. Apushkinskaya, Universität des Saarlandes:
Two-phase parabolic obstacle problem: Infinity-estimates for derivates of solutions
more ... Location
Freie Universität Berlin, 14195 Berlin, Arnimallee 3, Hinterhaus, Raum 130

Abstract
Consider the two-phase parabolic obstacle problem with non-trivial Dirichlet condition ?u ? ?tu = ?+?u>0 ? ???u<0 in Q=?×(0;T), u = ? on ?pQ. Here T<+?, ? ? Rn is a given domain, ?pQ denotes the parabolic boundary of Q, and ?{\textpm} are non-negative constants satisfying ?++??>0. The problem arises as limiting case in the model of temperature control through the interior. In this talk we discuss the L?-estimates for the second-order space derivatives D2u near the parabolic boundary ?pQ. Observe that the case of general Dirichlet data cannot be reduced to zero ones due to non-linearity and discontinuity at u=0 of the right-hand side of the first equation. The talk is based on works in collaboration with Nina Uraltseva.

Host
Freie Universität Berlin
WIAS Berlin
Universität Bonn
Monday, 06.02.2012, 18.00 Uhr (FUB-031): Oberseminar Numerische Mathematik/Scientific Computing
Y. Hu, Peking University:
The adaptive finite element method for the fourth order problem
more ... Location
Freie Universität Berlin, 14195 Berlin, Arnimallee 6, Raum: 031

Abstract
For the fourth order elliptic problem, the use of conforming finite element methods often leads to very expensive calculations due to the fact that rather high polynomials are required to fulfill the C^1 continuity of the ansatz functions. Therefore, most of popular finite element methods in the literature are the nonconforming finite element method. There are a lot of papers concerning a priori analysis of the nonconforming finite elements in the literature. However, there are few works concerning the adaptive finite element methods of the fourth order problem. One difficulty is that all of nonconforming finite element spaces for the fourth order elliptic problems can not contain a conforming subspace that has the minimal approximation, which causes the challenge for the a posteriori error analysis of the nonconforming methods. Another difficulty is that most of conforming/nonconforming finite element spaces for the fourth order elliptic problems are nonnested on successive meshes. The latter is the main barrier for the convergence analysis of the adaptive finite element methods. In this talk, we shall present some recent progress concerning the a posteriori error estimates of finite element methods for the Kirchhoff-Love plate problem and the convergence and optimality analysis of the corresponding adaptive algorithm. The result will go to the nonconforming Morley element and some conforming finite element methods. In addition, we will discuss state of art for this research field.

Host
FU, ZIB, WIAS, HU, TU, Uni Potsdam
Universität Leipzig
Tuesday, 07.02.2012, 17.15 Uhr (FUB-031): Oberseminar Nonlinear Dynamics
N. Uraltseva, St. Petersburg State University:
Two-phase parabolic obstacle problem: Regularity properties of the free boundary
more ... Location
Freie Universität Berlin, 14195 Berlin, Arnimallee 6, Raum: 031

Abstract
In this talk we describe the methods, developed in the last decade, for studying the regularity of the free boundary in the vicinity of branch points. These methods are based on the use of various monotonicity formulas, blow-up technique and some observations of geometric nature.

Host
Freie Universität Berlin
WIAS Berlin
Wednesday, 08.02.2012, 10.00 Uhr (WIAS-ESH): Forschungsseminar Mathematische Statistik
P. von Bülau/F. Kiraly, Technische Universität Berlin:
Stationary subspace analysis and ideal regression
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Joint work with Frank Meinecke, Duncan Blythe and K.-R. M?uller. In the rst part of this talk, we introduce Stationary Subspace Analysis (SSA) [1], a source-separation method which linearly factorizes observed data into stationary and non-stationary components. We present an SSA algorithm for the mean and covariance matrix, discuss conditions for identiability and our simulation results. In an application to EEG analysis, we demonstrate how SSA reveals meaningful stationary and non-stationary brain sources. In the second part of this talk, we present ideal regression, an algebraic-geometric approach to estimating polynomial relations. Ideal regression is a generalization of classical regression setups. We demonstrate how to obtain consistent estimators and how to prove properties for these estimators, using techniques from algebraic geometry. We present a set of possible applications, and show that SSA can be viewed as a special case of ideal regression [2], exhibiting an algorithmic estimator which we evaluate in simulations. References [1] von B?unau, P., Meinecke, F. C., Kiraly, F. J. and M?uller, K. R. Finding Stationary Subspaces in Multivariate Time Series. Phys. Rev. Lett. 103 (21):214101, 2009 [2] Kiraly, F. J., von B?unau, P., Meinecke, F. C., Blythe, D. A. J. and M?uller, K. R. Algebraic Geometric Comparison of Probability Distributions. Oberwolfach preprint (OWP) 2011-30, 2011.

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Wednesday, 08.02.2012, 17.00 Uhr (HU-Raum 1.115): Berliner Kolloquium Wahrscheinlichkeitstheorie
Dr. N. Perkowski, Humboldt-Universität zu Berlin:
Dominating risk free measures
more ... Location
HU, 12489 Berlin, Rudower Chaussee 25, Johann-von-Neumann Haus, Raum 1.115

Abstract
We prove that for locally bounded processes, absence of arbitrage of the rst kind is equivalent to the existence of a dominating local martingale measure. The Fundamental Theorem of Asset Pricing of Delbaen and Schachermayer states that for locally bounded processes there exists an equivalent local martingale measure if and only if the two conditions (NA) and (NA1) are satised. In a related work, Delbaen and Schachermayer show that for continuous processes, the condition (NA) implies the existence of an absolutely continuous local martingale measure. Here we complete this program, by proving that for locally bounded processes, (NA1) is equivalent to the existence of a dominating local martingale measure. This is motivated by and related to results from the theory of ltration enlargements. This is joint work with Peter Imkeller.

Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
Wednesday, 08.02.2012, 18.00 Uhr (HU-Raum 1.115): Berliner Kolloquium Wahrscheinlichkeitstheorie
Dr. P. Turkedjiev, Humboldt-Universität zu Berlin:
Approximation of discrete backward stochastic differential equations using a multi-step forward, empirical regression scheme
more ... Location
HU, 12489 Berlin, Rudower Chaussee 25, Johann-von-Neumann Haus, Raum 1.115

Abstract
We consider the dynamic programming equation arising from the time-discretization of backward stochastic dierential equations. The generator is assumed to be locally Lipschitz, which includes some cases of quadratic drivers. The sequence of conditional expectations is computed using empirical least-squares regres- sions. We provide full error estimates for this approximation depending on the time-grid, the number of simulations and the approximation spaces for regres- sion. Furthermore, we show that the Multi step-forward Dynamic Programming (MDP) equation yields better error estimates than the usual One-step forward DP (ODP) equation in the case where the generator and terminal condition are dierentiable. This is a joint work with Emmanuel Gobet

Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
Thursday, 09.02.2012, 14.00 Uhr (WIAS-ESH): Seminar Numerische Mathematik
Dr. R. Schneider, TU Dresden:
With edge based refinement towards anisotropic adaptive refinement in FEM
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We propose a new paradigm for adaptive mesh refinement. Instead of considering local mesh diameters and their adaption to solution features, we propose to evaluate the benefit of possible refinements in a direct fashion, and to select the most profitable refinements. We demonstrate that based on this approach a directional refinement of triangular elements can be achieved, allowing arbitrarily high aspect ratios.
However, only with the help of edge swapping and/or node removal (directional un-refinement) near optimal performance can be achieved for strongly anisotropic solution features. With these ingredients even re-alignment of the mesh with arbitrary error directions is achieved. Numerical experiments demonstrate the utility of the proposed anisotropic refinement strategy.

Host
WIAS Berlin
Wednesday, 15.02.2012, 15.15 Uhr (WIAS-ESH): BERLINER OBERSEMINAR Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)
Dr. T. Roubíček, Charles University, Prague, Czech Republic:
A model of rupturing lithospheric faults with re-occurring earthquakes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
hier

Further Informations
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Thursday, 16.02.2012, 16.15 Uhr (WIAS-ESH): Forschungsseminar Mathematische Modelle der Photonik
A. Pimenov, WIAS Berlin:
A Hermite-Galerkin method for numerical solution of a model of an inhomogeneously broadened semiconductor laser
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
Humboldt-Universität zu Berlin
WIAS Berlin
February 21 – 23, 2012 (WIAS-ESH): Workshop/Konferenz: From Particle Systems to Differential Equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
April 25 – 27, 2012 (WIAS-ESH): Workshop/Konferenz: Workshop on Adaptive Methods with Applications in Fluid Dynamics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
DFG Research Center MATHEON
DFG Schwerpunktprogram 1276
WIAS Berlin