Research Seminar
-
Numerical Analysis
SoSe 2024

Table of Contents


Organization [ back ]

Prof. Carsten Carstensen
Contact: Benedikt Gräßle (graesslb(at)math.hu-berlin.de)

The seminar talks usually take place on Wednesday at 13:00 c.t..

The announcements for each talk will be sent via a mailing list. Please subscribe via sympa or contact Benedikt Gräßle (graesslb(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
April 17, 2024 13:15 Carsten Carstensen
(HU Berlin) 		Discussion on duality in the Poisson model problem 2.417
April 17, 2024 15:15 Tim Stiebert
(HU Berlin) 		Guaranteed lower eigenvalue bounds via a conforming FEM 2.417
April 24, 2024 13:15 Christian Merdon
(WIAS Berlin) 		Pressure-robustness in Navier-Stokes simulations 2.417
Mai 08, 2024 13:15 Benedikt Gräßle
(HU Berlin) 		Inf-sup bounds for semilinear problems from nonconforming discretisations 2.417
Mai 13, 2024 15:15 Asha Dond
(IISER TVM) 		Quasi-optimality of adaptive FEMs for distributed elliptic optimal control problems 2.417
Mai 22, 2024 13:15 Ruma Maity
(Uni Innsbruck) 		Finite element methods for the Landau-de Gennes minimization problem of nematic liquid crystals 2.417
Mai 27, 2024 10:15 Carsten Carstensen
(HU Berlin) 		dG für garantierte untere bi-Laplace Eigenwertschranken online
Mai 29, 2024 13:15 Carsten Carstensen
(HU Berlin) 		A simple approach for companion operators for Crouzeix-Raviart finite element spaces with inhomogeneous Dirichlet boundary conditions 2.006
Juni 05, 2024 13:15 Benedikt Gräßle
(HU Berlin) 		Analysing WOPSIP by supercloseness 2.417
Juni 19, 2024 13:15 Tim Stiebert
(HU Berlin) 		Guaranteed lower eigenvalue bounds for the Schrödinger eigenvalue problem 2.417
July 01, 2024 13:15 Norbert Heuer
(PUC Chile) 		Abstrakte hybride Galerkin Methoden 2.417
July 03, 2024 13:15 Ngoc Tien Tran
(Uni Augsburg) 		Hybrid high-order method for the biharmonic eigenvalue problem 2.417
July 10, 2024 13:15 Lara Theallier
(HU Berlin) 		Lower energy bounds in the Landau-de Gennes model for nematic liquid crystals 2.417
Juli 17, 2024 13:15 Stefan Sauter
(Uni Zürich) 		The acoustic half space Green's function with impedance boundary condition in d spatial dimensions: Fast evaluation and numerical quadrature 2.417
This semester concluded with two one-day block seminars: The seminar Numerical Analysis in Leipzig and Berlin (NA-LaB) took place on August 06, 2024 and the workshop 2CCC was held on August 08, 2024.

Abstracts [ back ]

Speaker: Asha Dond
Title: Quasi-optimality of adaptive FEMs for distributed elliptic optimal control problems
In this talk, we will discuss the quasi-optimality of adaptive nonconform- ing finite element methods for distributed optimal control problems governed by m-harmonic operators for m = 1, 2. A variational discretization approach is employed and the state and adjoint variables are discretized using non- conforming finite elements. The general axiomatic framework that includes stability, reduction, discrete reliability, and quasi-orthogonality establishes the quasi-optimality. Numerical results demonstrate the theoretically pre- dicted orders of convergence.
Speaker: Ruma Maity
Title: Finite element methods for the Landau-de Gennes minimization problem of nematic liquid crystals
Nematic liquid crystals represent a transitional state of matter between liquid and crystalline phases that combine the fluidity of liquids with the ordered structure of crystalline solids. These materials are widely utilized in various practical applications, such as display devices, sensors, thermometers, nanoparticle organizations, proteins, and cell membranes. In this talk, we discuss finite element approximation of the nonlinear elliptic partial differential equations associated with the Landau-de Gennes model for nematic liquid crystals. We establish the existence and local uniqueness of the discrete solutions, a priori error estimates, and a posteriori error estimates that steer the adaptive refinement process. Additionally, we explore Ball and Majumdar's modifications of the Landau-de Gennes Q-tensor model that enforces the physically realistic values of the Q tensor eigenvalues. We discuss some numerical experiments that corroborate the theoretical estimates, and adaptive mesh refinements that capture the defect points in nematic profiles.
Speaker: Carsten Carstensen
Title: dG für garantierte untere bi-Laplace Eigenwertschranken
Quadratische diskontinuierliche Galerkin Verfahren sind simultan mit der Morley Finite-Elemente-Methode mit den Arbeiten mit N. Nataraj hinreichend verstanden. Die Morley Finite-Elemente-Methode erlaubt nach den Arbeiten mit D. Gallistl und S. Puttkammer verschiedene garantierte untere Eigenwertschranken. Die mathematischen Methoden dazu sollen nun zu neuen extra-stabilisierten diskontinuierlichen Galerkin Verfahren führen und damit diese Methodik auch für eine grosse Klasse von Nichstandardverfahren eröffnen. Der Vortrag beginnt mit einer Stabilisierung wie sie unlängst im J. Nummer. Math. erschienen ist bzw. auf Papier im August erscheinen wird für die C0IP jetzt angewendet auf die quadratischen diskontinuierlichen Galerkin Verfahren. Daraus resultiert eine Stabilisierung mit den Morley Funktionen im Kern. Das erlaubt eine saubere extra-stabilisierte diskontinuierliche Galerkin Methode die dann für hinreichend feine Netze direkt garantierte unter Eigenwertschranken berechnet. Weitere Anwendungen z.B. zur C0IP werden abschließend diskutiert. Die Anwendung auf eine zweite diskontinuierliche Galerkin Methode wird damit vielleicht auch möglich.
Speaker: Stefan Sauter
Title: The acoustic half space Green's function with impedance boundary condition in d spatial dimensions: Fast evaluation and numerical quadrature
In our talk, we introduce a representation of the acoustic half space Green's function with impedance boundary conditions in d space dimensions which avoids oscillatory Fourier integrals. A numerical quadrature method is developed for its fast evaluation. In the context of boundary element methods this function must be integrated over pairs of simplices and we present an efficient approximation method.

Archive [ back ]