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Archive 2025

Date / Time Speaker Title Location
26 February 2025
16:30-17:30 		Prof. Dr. Philippe Ciarlet
Institut für Mathematik, Universität Zürich
Event Details
Speaker invited by Prof. Dr. Stefan Sauter
Abstract As is well-known, Koiter's model is often used in numerical simulations, because it is a two-dimensional model that captures well the "membrane-dominated" and "flexural-dominated" effects that arise in a nonlinearly elastic shell subjected to applied forces and specific boundary conditions. Finding a satisfactory existence theory for this nonlinear shell model has stood as an open problem for a very long time. The present work, which is a joint work with Cristinel Mardare, provides a two-dimensional model that preserves all the virtues of Koiter's model, while being in addition amenable to a satisfactory existence theory. More precisely, our new two-dimensional mathematical model for a nonlinearly elastic shell takes the form of a minimization problem with a stored energy function that is polyconvex and orientation-preserving, and more generally satisfies all the other assumptions of John Ball's existence theorem. In addition, the most noteworthy feature of this model is that it is "of Koiter's type", in the sense that for a specific class of deformations that are "to within the first order" identical to those introduced by W.T. Koiter for defining his model, the "lowest order part" of its stored energy function coincides with the stored energy function of Koiter's model.
A two-dimensional nonlinear shell model of Koiter's type
HG G 19.2
12 March 2025
16:00-17:00 		Dr. Enrico Zampa
University of Vienna
Event Details
Speaker invited by Prof. Dr. Ralf Hiptmair
Abstract Incompressible magnetohydrodynamics (MHD) and the incompressible Godunov-Peshkov-Romenski (GPR) model share a similar structural framework, with key properties such as energy conservation, incompressibility, and involutions. In this talk, we demonstrate how to preserve these essential properties at the fully discrete level using compatible finite element methods, combined with a tailored time integration scheme. Furthermore, we explore both linear and nonlinear stabilization strategies necessary for convection-dominated regimes, examining their interplay with structure preservation. In particular, we show that such stabilizations affect only energy conservation. This research was conducted in collaboration with M. Dumbser from the University of Trento.
Structure-preserving discretization of incompressible magnetohydrodynamics and the incompressible Godunov-Peshkov-Romenski model
HG G 19.2
19 March 2025
16:30-17:30 		Prof. Dr. Tulin Kaman
University of Arkansas, USA
Event Details
Speaker invited by Prof. Dr. Ralf Hiptmair
Abstract Turbulent mixing induced by hydrodynamic instabilities occurs when two fluids of different densities, velocities, and viscosities interact. Theoretical, experimental, and numerical efforts to understand and predict the dynamics of hydrodynamic instabilities are very important for science and engineering applications. Statistical convergence and turbulence quantification are crucial for achieving reliable and accurate modeling and simulations. In this talk, we present an increasingly accurate and robust front-tracking/ghost-fluid method with higher-order weighted essentially non-oscillatory schemes used for the numerical simulations of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities. We investigate the time evolution of velocity fields and fluctuations for different configurations to explore the scaling law of the energy spectrum.
Statistical convergence of turbulence
HG G 19.2
26 March 2025
16:30-17:30 		Dr. Nicolas Boullé
Imperial College London
Event Details
Speaker invited by Prof. Dr. Rima Alaifari
Abstract There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint? Current practical approaches suggest that one can accurately recover an operator while only using data generated by the forward action of the operator without access to the adjoint. However, naively, it seems essential to sample the action of the adjoint for learning time-dependent PDEs. In this talk, we will first explore connections with low-rank matrix recovery problems in numerical linear algebra. Then, we will show that one can approximate a family of non-self-adjoint infinite-dimensional compact operators via projection onto a Fourier basis without querying the adjoint.
Operator learning without the adjoint
HG G 19.2
2 April 2025
16:30-17:30 		Prof. Dr. Pavel Exner
Nuclear Physics Institute of the CAS
Event Details
Speaker invited by Prof. Dr. Habib Ammari
Abstract The talk discusses a class of Sch¨odinger operators the potentials of which are channels of a fixed profile, focusing on relations between the spectrum of such an operator and the channel geometry. We provide different sufficient conditions under which a non-straight but asymptotically straight channel gives rise to a non-empty discrete spectrum. We also address the groundstate optimalization problem in case of a loop-shaped configuration, and consider a modification of the model where the channel is replaced by an array of potential wells, each exhibiting a rotational symmetry.
Localized states in soft waveguides and quantum dot arrays
HG G 19.2
9 April 2025
16:30-17:30 		Prof. Dr. Michael Dumbser
University of Trento
Event Details
Speaker invited by Prof. Dr. Rémi Abgrall
On well-balanced finite difference, finite volume and discontinuous Galerkin schemes for the Einstein-Euler system of general relativity
HG G 19.2
7 May 2025
16:30-17:30 		Ting Lin
Peking University
Event Details
Speaker invited by Prof. Dr. Ralf Hiptmair
Abstract We provide a finite element discretization of $\ell$-form-valued $k$ form in $n$ dimensions for general $k$, $\ell$ and $n$ and polynomial degree. The construction generalizes finite element Whitney forms for the de~Rham complex and their higher-order and distributional versions, the Regge finite elements and the Christiansen--Regge elasticity complex, the TDNNS element for symmetric stress tensors, the MCS element for traceless matrix fields, the Hellan--Herrmann--Johnson (HHJ) elements for biharmonic equations, and discrete divdiv and Hessian complexes in [Hu, Lin, and Zhang, 2025]. The construction discretizes the Bernstein--Gelfand--Gelfand (BGG) diagrams. Applications of the construction include discretization of strain and stress tensors in continuum mechanics and metric and curvature tensors in differential geometry in any dimension. This talk is based on a joint work with Kaibo Hu (Edinburgh).
Finite element form-valued forms: A unified construction
HG G 19.2
14 May 2025
16:30-17:30 		Prof. Dr. Michael Feischl
TU Wien
Event Details
Speaker invited by Prof. Dr. Christoph Schwab
Title T.B.A.
HG G 19.2
21 May 2025
16:30-17:30 		Dr. Martin Halla
Karlsruhe Inst. of Technology
Event Details
Speaker invited by Prof. Dr. Ralf Hiptmair
Title T.B.A.
HG G 19.2

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