Research Seminar
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Numerical Analysis
WiSe 2023/2024

Table of Contents


Organization [ back ]

Prof. Carsten Carstensen
Contact: Sophie Puttkammer (puttkams(at)math.hu-berlin.de)

The seminar talks usually take place on Tuesday at 11 am.

The announcements for each talk will be sent via a mailing list. Please subscribe via sympa or contact Sophie Puttkammer (puttkams(at)math.hu-berlin.de) if you want to join the list.

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
October 17, 2023 13:15 Christian Merdon
(WIAS Berlin) 		Gradient-robust hybrid discontinuous Galerkin discretizations for the compressible Stokes equations 2.417
October 24, 2023 11:15 Sophie Puttkammer
(HU Berlin) 		An enriched Crouzeix-Raviart FEM for guaranteed lower eigenvalue bounds 2.417
October 26, 2023 11:15 Felix Goldmann
(HU Berlin) 		Unstetige Galerkinverfahren für das parabolische Hindernisproblem online
October 31, 2023 11:15 Benedikt Gräßle
(HU Berlin) 		On nonconforming approximations for a class of semilinear problems 2.417
November 1, 2023 11:15 Tien Tran Ngoc
(Universität Augsburg) 		Lower eigenvalue bounds with hybrid high-order methods 2.417
November 7, 2023 11:15 Sophie Puttkammer
(HU Berlin) 		Notes on Morley FEM in 3D 2.417
November 13, 2023 11:00 Norbert Heuer
(Pontificia Universidad Católica de Chile) 		Normal-normal continuous symmetric stresses in  finite element elasticity 2.417
November 13, 2023 16:00 Neela Nataraj
(IIT Bombay) 		Adaptive Computation of Fourth-Order Problems 2.417
November 21, 2023 11:15 Georgi Mitsov
(HU Berlin) 		Time-space variational formulations for the heat equation 2.417
November 22, 2023 11:15 Lara Theallier
(HU Berlin) 		Hybrid-high-order methods for linear elasticity 2.417
November 23, 2023 11:15 Quanling Deng
(Australian National University) 		Particle-Continuum Multiscale Modeling of Sea Ice Floes 2.417
November 28, 2023 11:15 Julia Schaeffer
(HU Berlin) 		Contour integration methods for nonlinear eigenvalue problems in nanooptics 2.417
December 1, 2023 10:00 Carsten Carstensen
(HU Berlin) 		Hs(Ω) for 0<s<1 3.008
December 5, 2023 11:15 Johannes Storn
(Universität Bielefeld) 		Adaptive Mesh Refinement for arbitrary initial Triangulations 2.417
December 8, 2023 13:15 Carsten Carstensen
(HU Berlin) 		Hs(Ω) for 0<s<1 (Fortsetzung) 3.006

Abstracts [ back ]

Speaker: Christian Merdon
Title: Gradient-robust hybrid discontinuous Galerkin discretizations for the compressible Stokes equations
The talk introduces the concept of gradient-robustness for the velocity-density formulation of the compressible Stokes and its connection to the preservation of certain well-balanced states. Gradient-robust hybrid discontinuous Galerkin (HDG) discretisations of arbitrary order are discussed. The lowest-order scheme is shown to be non-negativity preserving and, at least in the isothermal case with linear equation of state, to be stable and provably convergent. The gradient-robustness property dramatically enhances the accuracy in well-balanced situations, such as the hydrostatic balance where the pressure gradient balances the gravity force, but also in non-hydrostatic cases for low Mach numbers and small viscosities. This is demonstrated in some numerical examples.

(joint work with Philip Lederer)
Speaker: Quanling Deng
Title: Particle-Continuum Multiscale Modeling of Sea Ice Floes
In this talk, I will start by presenting some quick facts about Arctic and Antarctic sea ice floes followed by a quick overview of the major sea ice continuum and particle models. I will then present our main contribution to its multiscale modelling.

The recent Lagrangian particle model based on the discrete element method (DEM) has shown improved model performance and started to gain more attention from groups that are working on Global Climate Models (GCMs). We adopt the DEM model for sea ice dynamical simulation. The major challenges are 1) model coupling in different frames of reference (Lagrangian for sea ice while Eulerian for the ocean and atmosphere dynamics); 2) the heavy computational cost when the number of the floes is large; and 3) inaccurate floe parameterisation when the floe distribution has multiscale features. To overcome these challenges, I will present a superfloe parameterisation to reduce the computational cost and a superparameterisation method to capture the multiscale features. In particular, the superfloe parameterisation facilitates noise inflation in data assimilation that recovers the unobserved ocean field underneath the sea ice. To capture the multiscale features, we adopt the Boltzmann equation for particles and superparameterise the sea ice floes as continuity equations governing the statistical moments. This leads to a particle-continuum coupled multiscale model. I will present several numerical experiments to demonstrate the success of the proposed method.

This is joint work with Sam Stechmann (UW-Madison) and Nan Chen (UW-Madison).
Speaker: Johannes Storn
Title: Adaptive Mesh Refinement for arbitrary initial Triangulations
This talk introduces a simple initialization of the Maubach/Traxler bisection routine for adaptive mesh refinements. This initialization applies to any conforming initial triangulation. It preserves shape-regularity, satisfies the closure estimate needed for optimal convergence of adaptive schemes, and allows for the intrinsic use of existing implementations.

This talk results from joint work with Lars Diening (Bielefeld University) and Lukas Gehring (Friedrich-Schiller-Universität Jena).

Archive [ back ]