Research Seminar
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Numerical Analysis
SoSe 2026

Table of Contents


Organization [ back ]

Prof. Carsten Carstensen
Contact: Tim Stiebert (stiebert@math.hu-berlin.de)

The seminar talks usually take place on Tuesday at 13 c.t..

Location [ back ]

Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin
House 2, Floor 4, Room 2.417

Schedule [ back ]

Date Time Talk by Title Room
14.04.2026 13:15 Georgi Mitsov
(HU Berlin) 		Inf-sup constants for interface problems 2.417
21.04.2026 13:15 Nathan Arnaud
(HU Berlin) 		Crouzeix-Raviart FEM for the Poisson problem with singular data 2.417
21.04.2026 14:15 Yuyang Guo
(Peking University) 		Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors 2.417
28.04.2026 13:15 Lara Theallier
(HU Berlin) 		Nonconforming approximation of Ginzburg-Landau-type semilinearities 2.417
05.05.2026 13:15 Tim Stiebert
(HU Berlin) 		Guaranteed inf-sup bounds and their applications 2.417
12.05.2026 13:15 Theophile Chaumont-Frelet
(Centre Inria de l'Universite de Lille) 		Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality 2.417
19.05.2026 13:15 Julia Schäffer
(HU Berlin) 		TBA 2.417
26.05.2026 13:15 Konstantin Viol
(HU Berlin) 		TBA 2.417

Abstracts [back]

Speaker: Yuyang Guo (Peking University)
Title: Discretizing linearized Einstein-Bianchi system by symmetric and tracelsess tensors
The Einstein-Bianchi system reformulates Einstein's field equations with symmetric and traceless tensors. Linearization around the trivial Minkowski metric leads to a Maxwell-type system, analogous to the equations governing the electric and magnetic field vectors. Despite its resemblance to Maxwell's equations, an essential difference is that the unkowns E and B are symmetric and traceless matrices rather than vectors. This disctinction presents a significant challenge in constructing stable finite element methods.
The presentation proposes a new formulation that treats the linearized Einstein-Bianchi system as the Hodge wave equation associated with the conformal Hessian complex. To discretize this equation, a conforming finite element conformal Hessian complex that preserves symmetric and traceless-ness simultaneously is constructed on general three-dimensional tetrahedral grids, and its exactness is proved.
Speaker: Lara Theallier (HU Berlin)
Title: Nonconforming approximation of Ginzburg-Landau-type semilinearities
The Landau-de Gennes model for nematic liquid crystals provides computational challenges within a non-convex minimization problem. The associated Euler-Lagrange equations form a semilinear second-order elliptic boundary value problem with reduced regularity in non-convex domains as well as additional topological singularities called voritices. The energy landscape in this non-convex minimisation problem is unexpectedly rich with many stationary points of the energy functional and severe difficulties for the local solve. Nonconforming Crouzeix-Raviart finite elements allow for lower energy bounds in the asymptotic range of sufficiently fine meshes.
The presentation departs with 2D computational benchmark examples and explains the origin of vortex singularities for Dirichlet data of non-zero winding number for larger Ginzburg parameters l for this is a novel aspect in the mandatory adaptive mesh-refining. A priori existence of discrete solutions and their weak or strong (global) convergence towards stationary points along subsequences is illuminated. An asymptotic a priori and a posteriori local error analysis with optimal rates for appropriate adaptive algorithms concludes the presentation.
Speaker: Theophile Chaumont-Frelet (Centre Inria de l'Universite de Lille)
Title: Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality
I will present an algorithm to numerically determine whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This class of problems is relevant in many contexts, in particular to model time-harmonic wave propagation phenomena. The algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which may in turn be used for a posteriori estimation purposes, thereby enabling fully-guaranteed error bounds for finite element discretizations. This numerical lower bound is based on two discrete singular value problems involving a Lagrange finite element discretization coupled with an a posteriori error estimator based on flux reconstruction techniques. I will show that if the finite element discretization is sufficiently rich, the proposed lower bounds underestimates the optimal inf-sup constant only by a factor roughly equal to two at most, and I will present numerical examples highlighting this result in practice.

Archive [ back ]