Research Seminar
WS 2019/20
Table of Contents
Organization [ back ]
Prof. Carsten Carstensen
Contact: Sophie Puttkammer (puttkams(at)math.huberlin.de)
Location [ back ]
HumboldtUniversität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin
Room 2.417 or Room 3.007
Gallery [ back ]
Schedule [ back ]
Date  Time  Talk by  Title  Room 

October 16, 2019  11:15  Georgi Mitsov (HU Berlin) 
On the wellposedness of a generalized dPG timestepping methods for the heat equation  3.007 
October 23, 2019  11:15  Julian Streitberger (HU Berlin) 
Two Lowest Order MFEM Examples  2.417 
October 23, 2019  11:45  Sophie Puttkammer (HU Berlin) 
A modified HHO method to compute guaranteed lower eigenvalue bounds  2.417 
October 29, 2019  11:15  Tim Ricken (Universität Stuttgart) 
Neue Methoden zur Modellierung von Mehrphasenmaterialien mit Mehrskalenansätzen  Anwendungsbeispiele aus den Bereichen Materialwissenschaft, Biomechanik und Umwelttechnik  2.417 
October 30, 2019  11:15  Tien TranNgoc (HU Berlin) 
HHO methods for a class of degenerate convex minimization problems  3.007 
October 31, 2019  9:30  Max Gunzburger (Florida State University) 
Integral equation modeling for anomalous diffusion and nonlocal mechanics  2.417 
November 6, 2019  11:15  Julia Schäffer (HU Berlin) 
Convergence rates for the FEAST algorithm with dPG resolvent discretization  2.417 
November 6, 2019  14:45  Neela Nataraj (IIT Bombay) 
Finite element methods for nematic liquid crystals  2.417 
November 13, 2019  11:15  Ornela Mulita (SISSA) 
Smoothed Adaptive Finite Element Methods  2.417 
November 20, 2019  11:15  Ma Rui (HU Berlin) 
Convergence of the adaptive nonconforming element method for an obstacle problem  2.417 
November 27, 2019  15:00  Stefan Sauter (Universität Zürich) 
𝒟ℋ^{2} Matrices and their Application to Scattering Problems  2.417 
December 4, 2019  11:15  Céline Torres (Universität Zürich) 
Stability of the Helmholtz equation with highly oscillatory coefficients  2.417 
December 11, 2019  11:15  Benedikt Gräßle (HU Berlin) 
Numerical Analysis with HHO methods  2.417 
December 18, 2019  11:00  Henrik Schneider (HU Berlin) 
DPG for the Laplace eigenvalue problem  2.417 
January 8, 2020  11:15  Sophie Puttkammer (HU Berlin) 
Remarks on optimal convergence rates for guaranteed lower eigenvalue bounds with a modified nonconforming method  2.417 
January 10, 2020  13:00  Oliver Sander (TU Dresden) 
Geometric Finite Element  3.008 
January 15, 2020  11:15  Philipp Bringmann (HU Berlin) 
Convergence proofs for adaptive LSFEMs and implementation of the octAFEM3D software package  2.417 
January 22, 2020  11:15  Joscha Matysiak (HU Berlin) 
This presentation is rescheduled on February 12th.  
January 29, 2020  11:15  Georgi Mitsov (HU Berlin) 
Wellposedness of generalized dPG methods with locally weighted testsearch norms for the heat equation  3.007 
January 29, 2020  16:15  Alexander Heinlein (Universität zu Köln) 
Overlapping Schwarz preconditioning techniques for nonlinear problems  2.417 
January 31, 2020  13:30  Philipp Bringmann (HU Berlin) 
Adaptive leastsquares finite element method with optimal convergence rates  2.417 
February 12, 2020  11:15  Joscha Matysiak (HU Berlin) 
TBA  TBA 
Abstracts [ back ]
Speaker:  Max Gunzburger 

Title:  Integral equation modeling for anomalous diffusion and nonlocal mechanics 
We use the canonical examples of fractional Laplacian and peridynamics equations to discuss their use as models for nonlocal diffusion and mechanics, respectively, via integral equations with singular kernels. We then proceed to discuss theories for the analysis and numerical analysis of the models considered, relying on a nonlocal vector calculus to define weak formulations in function space settings. In particular, we discuss the recently developed asymptotically compatible families of discretization schemes. Brief forays into examples and extensions are made, including obstacle problems and wave problems.  
Speaker:  Neela Nataraj 
Title:  Finite element methods for nematic liquid crystals 
We consider a system of second order nonlinear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element methods are used to approximate the solutions of this nonlinear problem
with nonhomogeneous Dirichlet boundary conditions. A discrete infsup condition demonstrates the stability of the discontinuous Galerkin discretization of a wellposed linear problem. We then establish the existence and local uniqueness of the discrete solution of the nonlinear problem. An a priori error
estimate in the energy norm is derived and the quadratic convergence of Newton’s iterates is illustrated.
This is a joint work with Ruma Maity and Apala Majumdar. 

Speaker:  Ornela Mulita 
Title:  Smoothed Adaptive Finite Element Methods 
We propose a new algorithm for Adaptive Finite Element Methods based on Smoothing iterations (SAFEM). The algorithm is inspired by the ascending phase of the Vcycle multigrid method: we replace accurate algebraic solutions in intermediate cycles of the classical AFEM with the application of a prolongation step, followed by a fixed number of few smoothing steps. The method reduces the overall computational cost of AFEM by providing a fast procedure for the construction of a quasioptimal mesh sequence with large algebraic error in the intermediate cycles. Indeed, even though the intermediate solutions are far from the exact algebraic solutions, we show that their aposteriori error estimation produces a refinement pattern that is substantially equivalent to the one that would be generated by classical AFEM, at a considerable fraction of the computational cost. In this talk, we will quantify rigorously how the error propagates throughout the algorithm, and then we will provide a connection with classical a posteriori error analysis. Finally, we will present a series of numerical experiments that highlights the efficiency and the computational speedup of SAFEM.  
Speaker:  Stefan Sauter 
Title:  𝒟ℋ^{2} Matrices and their Application to Scattering Problems 
The sparse approximation of highfrequency Helmholtztype integral operators has many important physical applications such as problems in wave propagation and wave scattering. The discrete system matrices are huge and densely populated; hence their sparse approximation is of outstanding importance. In our talk we will generalize the directional ℋ^{2}
matrix techniques from the "pure" Helmholtz operator
$Lu=\Delta u+{z}^{2}u$
with $z=ik;\phantom{\rule{0.222em}{0ex}}k$
real, to general complex frequencies $z$
with $Re\left(z\right)>0$.
In this case, the fundamental solution decreases exponentially for large arguments. We will develop a new admissibility condition which contain
$Re\left(z\right)$
and $Im\left(z\right)$ in an explicit way and introduce the approximation of the integral kernel function on admissible blocks in terms of frequencydependent directional expansion functions. We present an error analysis which is explicit with respect to the expansion order and with respect to the real and imaginary part of $z$. This allows us to choose the variable expansion order in a quasioptimal way depending on $Re\left(z\right)$ but independent of, possibly large, $Im\left(z\right)$. The complexity analysis is explicit with respect to $Re\left(z\right)$ and $Im\left(z\right)$ and shows how higher values of $Re\left(z\right)$ reduce the complexity. In certain cases, it even turns out that the discrete matrix can be replaced by its nearfield part.
Numerical experiments illustrate the sharpness of the derived estimates and the efficiency of our sparse approximation. This talk comprises joint work with S. Börm, ChristianAlbrechtsUniversität Kiel, Germany and M. LopezFernandez, Sapienza Universita di Roma, Italy. 

Speaker:  Céline Torres 
Title:  Stability of the Helmholtz equation with highly oscillatory coefficients 
Existence and uniqueness of the heterogeneous Helmholtz problem on bounded domains can be shown using a unique continuation principle in Fredholm's alternative. This results in an energy estimate of the problem, with a stability constant that is not directly explicit in the coefficients or the wave number. We show, that for highly oscillatory coefficients, the solution can exhibit a localised wave. As a result the stability grows exponentially in the wave number. We discuss how this constant enters in the condition for quasioptimality, when using a hpFinite Element Method to discretise the problem and the difficulties that arise therein. 
Archive [ back ]
 Current Seminar
 Summer Semester 2019
 Winter Semester 2018/2019
 Summer Semester 2018
 Winter Semester 2017/2018
 Summer Semester 2017
 Winter Semester 2016/2017
 Summer Semester 2016
 Winter Semester 2015/2016
 Summer Semester 2015
 Winter Semester 2014/2015
 Summer Semester 2014
 Winter Semester 2013/2014
 Summer Semester 2013
 Winter Semester 2012/2013
 Summer Semester 2012
 Winter Semester 2011/2012
 Summer Semester 2011