Dependency of the coefficients in an asymptotic expansion for the weak error, demonstrating that the convergence to 2nd order is exponentially rapid in time. WIAS Berlin Donnerstag, 16. Seminar Nichtlineare Optimierung und Inverse Probleme Dr. WIAS Berlin Donnerstag, 16. surfaces, and engineering analysis. the NURBS basis functions that describe the geometry define also the approximation spaces. methods, providing a tool for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. WIAS Berlin Mittwoch, 15. Universität zu Berlin Mittwoch, 15. Forschungsseminar Mathematische Statistik Dr. specified model, or the parameter corresponding to the best approximating model from the considered parametric family for a misspecified model, occurs on the boundary of the parameter space. has a faster rate of convergence in the directions of the Gamma distribution components.
One implication of this result is that for some models, there appears to be no lower bound on efficiency of estimating the unknown parameter if it is on the boundary of the parameter space. will discuss how this result can be used for identifying misspecification in regular models. The results will be illustrated on a problem from emission tomography. Universität zu Berlin Universität Potsdam Dienstag, 14. Seminar Nichtlineare Optimierung und Inverse Probleme Dr. The recovery scheme works in a rather general setting and possesses several salient features. space above the anomalies, and works independently of the physical properties of the anomalies. There might be anomalous components of multiscale sizes presented simultaneously.
Moreover, the proposed scheme is of a totally direct nature without any inversion involved, and hence it is very fast and robust against measurement noise. Both theoretical foundation and numerical experiments are presented. This extends related results in the literature on recovering multiscale scatterers located in homogeneous space. WIAS Berlin Dienstag, 17. Seminar Nichtlineare Optimierung und Inverse Probleme Prof.
WIAS Berlin University of Lugano Dienstag, 10. assembly is a mechanism responsible for the formation of complex structures through multiple interactions among the microscopic components of the system. We show that the occurring locking effects enable a control mechanism for the pattern formation process. dimensional case the parameter range in which patterns are created can be increased and the properties of occurring structures can be adjusted in a broader range. dimensional structures, including oblique and lattice patterns. In addition, a different control mechanism by means of a modulated transfer velocity is discussed. Our theoretical results predict that this method can also be used as an effective tool to control the pattern formation process.
WIAS Berlin Freitag, 06. known result by Buttazzo and Dal Maso. Moreover we will discuss how surgery methods can be used when a perimeter contraint is added. At the end, we will give some informations on the regularity of the eigenfunctions on optimal domains. WIAS Berlin Mittwoch, 04. How do cracks propagate?
Some ideas related to the energy criterion. Universität zu Berlin Dienstag, 03. Seminar Numerische Mathematik Prof. The construction of surrogate models is a crucial step for bringing computational tools to practical applications within an appropriate timeline. This can be accomplished by taking advantage of specific features of the problem at hand. the local dynamics are expected to develop mainly along a dominant direction.
The interaction between the local and network dynamics calls often for appropriate model reduction techniques. reduction, devised to deal with problems characterized by a prevalent dynamics, even though the presence of transverse dynamics may be locally significant. Moving from the original approach where we employ the same number of modes on the whole domain, we have successively introduced a more sophisticated approach, by automatically adapting the number of the modal functions according to the local level of complexity of the problem. time mesh is also accomplished. Institut für Klimafolgenforschung Donnerstag, 12. Universität zu Berlin WIAS Berlin Mittwoch, 11. Universität zu Berlin Mittwoch, 11. Liquid crystals are matter in a state between liquid and solid.
They flow like a liquid, but their molecular structure is similar to that of a solid crystal. In the most common nematic phase, molecules possess an orientation but no positional order. Stokes equations coupled with a diffusion equation governing the behavior of the direction field. We analyze some Ericksen Leslie systems in a quasilinear setting. We also investigate stability of equilibria with the generalized principle of linearized stability, obtain global existence of strong solutions which are eventually bounded on their maximal existence interval and discuss regularizing effects. WIAS Berlin Dienstag, 10. WIAS Berlin Dienstag, 10. Seminar Numerische Mathematik Prof.
phase Darcy flows in discrete fracture networks taking into account the mass exchange between the matrix and the fracture. We consider the asymptotic model for which the fractures are represented as interfaces of codimension one immersed in the matrix domain, leading to the so called hybrid dimensional Darcy flow model. The pressures at the interfaces between the matrix and the fracture network are continuous corresponding to a ratio between the normal permeability of the fracture and the width of the fracture assumed to be large compared with the ratio between the permeability of the matrix and the size of the domain.
schemes to the case of hybrid dimensional Darcy flow models. approaches, the VAG scheme has the advantage to avoid the mixing of the fracture and matrix rock types at the interfaces between the matrix and the fractures, while keeping the low cost of a nodal discretization on unstructured meshes. The convergence of the gradient schemes is obtained for two phase flow models under the assumption that the relative permeabilities are bounded from below by a strictly positive constant. This assumption is needed in the convergence proof only in order to take into account discontinuous capillary pressures in particular at the matrix fracture interfaces. The efficiency of our approach is shown on numerical examples of fracture networks in 2D and 3D. WIAS Berlin Dienstag, 10. Seminar Thermodynamische Modellierung und Analyse von Phasenübergängen Prof.
WIAS Berlin Donnerstag, 05. Forschungsseminar Mathematische Modelle der Photonik Dr. Universität zu Berlin WIAS Berlin Mittwoch, 04. Universität zu Berlin Mittwoch, 04. Our approach is geometric and based on considerations in Hilbert spaces. or in which the number of components increases with the sample size. dimensional but sparse additive models. Universität zu Berlin Universität Potsdam Dienstag, 03. In this talk we present a specially designed control variates for estimating smooth terminal functionals of discretized paths, arising from SDE path approximation. We discuss the additional gains, one can achieve via using weak schemes combined with our control variates for SMC path simulation method.
Our results are illustrated by several numerical examples. WIAS Berlin Donnerstag, 29. Universität zu Berlin WIAS Berlin Mittwoch, 28. Forschungsseminar Mathematische Statistik Prof. dimensional vector from linear observations that are corrupted by additive Gaussian white noise. Many solution approaches for such problems construct an estimate as the most regular element satisfying a bound on the coefficients of the residuals with respect to some frame. In order that the true parameter is feasible, the coefficients of the noise must satisfy the bound.
For that purpose we compute the asymptotic distribution of these coefficients. We show that generically a standard Gumbel law results, as it is known from the case of orthonormal bases. However, for highly redundant frames other limiting laws may occur.
We discuss applications of such results for thresholding in redundant wavelet or curvelet frames, and for the Dantzig selector. Universität zu Berlin Universität Potsdam Dienstag, 27. Oberseminar Nonlinear Dynamics Prof. modes, nodes, volume elements, etc. without assuming the existence of an inertial manifold. WIAS Berlin Freie Universität Berlin Dienstag, 27. WIAS Berlin European Research Council Donnerstag, 22. We introduce Lagrange finite element spaces adapted to approximate the slip condition. grid effects are modeled by an eddy diffusion term that acts only on a range of small resolved scales.
grid eddy viscosity term. We prove stability and convergence for solutions that only need to bear the natural minimal regularity, in unsteady regime. We also study the asymptotic energy balance of the system.
We finally include some numerical tests to assess the performance of the model described in this work. WIAS Berlin Mittwoch, 21. Universität zu Berlin Mittwoch, 21. Forschungsseminar Mathematische Statistik Dr.