Work group
current PhD students
Claudius Birke ideal MHD, low Mach & well-balanced schemes, astrophysical applications - joint project with Fritz Röpke (Heidelberg)
Kathrin Hellmuth inverse problems for kinetic equations in the context of chemotaxis
Eva Horlebein convergence of approximate solutions to the compressible multi-dimensional Euler equations
Lena Baumann a numerical reduced order approach applied to inverse probelms for kinetic equations
Jayesh Badwaik moving mesh method in two space dimensions for the Euler equations - uncertainty quantification for conservation laws
current Master-thesis students
Yu-Chen Cheng central schemes and well-balancing of Euler with gravity
Veronika Mayerhofer modelling flow in a network of channels, theory and numerics (jointly with Ulrik Fjordholm, Oslo)
Christine Barko modeling flow in a Tokamak: the semi-Lagrange method for kinetic equations
Moritz Beck inverse problems for kinetic equations made efficient by machine learning
Sebastian Schmidt structure preserving schemes
Gerhard Dill Anwendung von Machine Learning auf Schichtdickenmessung von Kunststoff-Muffen mit Radar (mit dem Kunststoff-Zentrum SKZ)
Marius Volpert numerical implementation of Guermond's invariant domain preserving algorithm
Luis Kaiser numerical wave propagation aided by machine learning
Amelie Gehring kinetic equations
Janina Kern numerical methods for conservation laws
current Bachelor-thesis students
Sophie Lauer singuläre Grenzwerte der kompressiblen Eulergleichungen
Tim Winkler deriving the Euler equations
some former Master-thesis students
Kai Ulrich A Dynamical Low-Rank Algorithm for a Kinetic Model for Gas Mixtures
Jonas Jackwirth Uncertainty Quantification for the Korteweg-de Vries equation
Vanessa Halat The Optimal Velocity Model - From microscopic to macroscopic traffic flow and the impact of autonomous vehicles on traffic flow
Claudia Knorr "On numerical methods for astrophysical flow" (numerical parameter study with the astrophysics code by Fritz Röpke)
Sonja Leicht Numerical simulations of elastic bodies
Julian Meusel Writing Einstein’s field equations as a hyperbolic first-order system in the CCZ4 formulation
Teresa Full The Semi-Lagrange Numerical Method for the Vlasov-Poisson Equation and Other Kinetic Equations
Mattis Vogelsang modeling plasma via multi-species kinitic equtions
Lena Baumann On Landau damping for the Vlasov-Poisson-BGK equation coupled with a BGK relaxation term
Winnie Hartwig invariant domain preserving schemes for hyperbolic conservation laws
Lukas Berberich uncertainty quantification for elasticity equations
Kardelen Koc stationarity preserving schemes for hyperbolic equations
Lukas Baumgärtner (jointly with Stephan Schmidt) total generalized variation on triangular meshes on surfaces
Kathrin Hellmuth (Computing the Black Scholes equation with uncertain volatility using the stochastic Galerkin method and a Bi-Fidelity approach see pdf of thesis )
Tobias Herzing (On hypocoercivity for a kinetic BGK equation with uncertainty)
Si-qi Wang (stochastic modeling of financial mathematics)
Alexander Hefter (relaxation approximation for the Euler equations)
Stefan Pröstler (uncertainty quantification for the KDV equation)
Lukas Thanhäuser (a kinetic relaxation scheme for magnetohydrodynamics)
Sandra Warnecke (on inverse problem for objects that move during the data acquisition process)
Jonathan Hohm (a multi-dim. scheme by Phil Roe for the 2-d compressible Euler equations)
Yannik Gleichmann (using Kutznetsov’s lemma for convergence rates of approximations to conservation laws)
Martin Müller (numerics for a multi-species kinetic model by Marlies Pirner)
Nicole Scheller (uncertainty quantification for scalar conservation laws)
Daniela Sittig (mathematical finance, in cooperation with the Deutsche Bank, modeling interest rates in a negative interest rate environment)
Jonas Berberich (co-advisor w. Fritz Röpke) (low Mach number simulations coupled with well-balanced methods)
Simon Markfelder (non-uniqueness of the 2-d compressible Euler equations)
Marie Meltzer Multispecies traffic models based on the Lighthill- Whitham and the Aw-Rascle model, see PDF of the thesis
Dominik Zoar (numerics for conservation laws, relaxation approach)
Michael Huber Numerische Algorithmen zur Bewertung von Finanzderivaten
Ellen Komber (numerical simulations of traffic flow on roads with junctions)
Johannes Löbbert (implementation of discontionuous Galerkin with adaptive mesh refinement for compressible Euler in the DUNE framework)
Marlies Pirner (A consistent kinetic model for a two-component mixture with an application to plasma)
Frank Pörner (On the involution constraint of a DG implementation for ideal MHD)
Carolin Apfel (als Praktikantin der Deutschen Bank): Stochastische Modelle zur Bewertung von Zinsderivaten
some former Diplom-thesis students
Astrid Thiemer (finite element simulation for non-Newtonian flow)
Oliver Mitesser (Micro- and macroscopic models of traffic flow)
Detlev Pabst (Solving the Euler equations using a relaxation approach, jointly w. Frederiqe Coquel)
Stephan Grosskinsky (A rigorous derivation of Smoluchowski’s equation in the moderate limit)
Alexander Linke (traffic flow at junctions)
Ruediger Back
Stephan Griebel
Hoffmann-Guben (generic non-existence of smooth flow around an airfoil with an angle of inclination)
Nadine Even (hydrodynamic limits)
Carsten Eberlein
Christine Dietrich
some former Bachelor-thesis students
Robin Novak Introduction to the Partial Differential Equations of Gas Dynamics & Their Numerical Solution
Johannes Rieger Herleitung der Black-Scholes-Formeln zur Bepreisung von europäischen Optionen
Moritz Marthy Herleitung der Black-Scholes-Merton-Formel über risikoneutrale Preismaße
Marvin Raab Lévyprozesse und deren Anwendung in der Finanzmathematik
Jonas Dornbusch Verkehrsflussmodelle und deren Numerik
Veronika Mayerhofer shallow water equations, numerical simulations, Tsunami modeling
Janina Kern deriving the Euler equations
Jonas Schlecht An asymptotic preserving scheme for the BGK model of the Boltzmann model
Lukas Krines Numerik stochastischer Differentialgleichungen
Fridolin Popov On the motion of cells a mathematical modelling approach
Marius Volpert Numerik der Euler- und MHD Gleichungen
Anna Lentz Finite-Volumen-Verfahren mit Well-Balancing zur Lösung der Eulergleichungen
Marc Scheller Zulassungarbeit: Kontinuierliche Altersstrukturmodelle
Moritz Beck (machine learning in cooperation with the company "Wölfel")
Maximilian Schemel (Modellierung von Erdöl Reservoiren mit der Buckley-Leverett Gleichung)
Markus Bott (interest derivatives in mathematical finance)
Hanna Weinmann (numerical methods for conservation laws)
Sonja Altenhöfer (Navier-Stokes equations and its discretization)
Jonas Fehn (stochastische Integrationstheorie)
Rosina Ziegler (Modelliering amerikanischer Optionen)
Lukas Baumgärtner (finite volume methods for conservation laws, CLAW PACK)
Philipp Haid (On stochastic integration)
Winnie Hartwig (existence of solutions to 1-d systems of conservation laws)
Maximilian Schell (Die Gleichungen der Fluid Mechanik)
Philip Haid (stochastic analysis)
Anja Katzenberger (Kurzkov’s theory)
Matthis Vogelsang (shape from shading: computing the three-dimensional shape of a surface from one image of that surface)
Jonas Jackwirth (Finanzmathematik: Einführung in Zinsderivate )
Maximilian Lorenz (Finanzmathematik)
Niklas Götz (Positivitätserhaltendene nodale discontinuous Galerkin Methoden hoher Konvergenzordnung für die ein-dimensionalen Eulergleichungen)
Niklas Hess Lineare partielle Differentialgleichungen, hyperbolisch, parabolisch und elliptisch
Jonathan Hohm Herleitung der partiellen Differentialgleichungen der Strömungsmechanik
Toni Greif Bewertung von Finanzderivaten mittels der Monte-Carlo-Methode im Vergleich mit weiteren numerischen Verfahren
Stefan Pröstler Einführung in die Fluidbewegung mit Ziel der Prandtlschen Grenzschichtgleichungen
Kai Günder Finanzmathematik: die stochastischen Grundlagen der Black Scholes Gleichung
Fabian Bleitner lineare hyperbolische Systeme nach Peter Lax
Jan Scherz an alternative proof of Glimm’s theorm using front tracking
Lukas Thanhäuser constructing weak solutions to hyperbolic conservation laws
Fabian Bleitner linear hyperbolic systems following Peter Lax
Martin Müller finite volume method for conservation laws and CLAWPACK
Sandra Warnecke (Boltzmann equation and Chapman Enskog expansion)
Theresa Christ (admissibility conditions in conservation laws using the book by Defermos)
Sasha-André Reus (Höhere Ordnung Finite-Volumen-Verfahren und ihre Anwendung in einem astrophysikalischen Code)
Peter Hohl (Finite Volumen Verfahren für Erhaltungsgleichungen auf einem sich bewegenden Gitter)
Alexander Hefter (implementing a well-balanced relaxation method for Euler with gravity into Clawpack)
Benedikt Hurle (conservation laws with source termes)
Simon Markfelder (Kruzkov well posedness for scalar conservation laws)
Marie Meltzer (traffic modeling)
Marlies Pirner (Boltzmann equations)
Jens Klotzky (Riemann problem)
Frank Pörner (Tsunami modeling)
Andreas Preiß (On the Hydrodynamic Limit of a Symmetric Simple Exclusion Process)
Philipp Schmitt (jointly with Haye Hinrichsen) (microscopic and macroscopic modeling of conservation laws with discontinuous flux)
Daniela Sittig (the Feymann-Kac formula and the heat equation)
Nadia Jammal (On modeling Tsunami waves)
Jeanette Hitzinger (mathematical finance)
former PhD students
Italo Vecchi (1989), Entropy Compactification for Nonlinear Hyperbolic Problems
Xiaoming Gu (1997), Exact Controllability for Several Models of Multidimensional Structures
Roland Völker (2002), Modeling protostellar jets
Jan Pfannes (2006), Thermonuclear explosions of rapidly rotating white dwarfs
Andreas Maier (2007), Large eddy simulations in astrophysics
Knut Waagan (2007), An approximate Riemann solver for MHD
Markus Hupp (2008), Turbulence driven star formation in disk galaxies
Nadine Even (2009), Hydrodynamic limits and conservation laws download here
Alejandro Bolanos Rosales (2016) (co-advisor w. Fritz Röpke) Low Mach Number Simulation of Convective Boundary Mixing in Classical Novae
Gero Schnücke (2016) Arbitrary Lagrangian-Eulerian Discontinuous Galerkin methods for nonlinear time-dependent first order pdes download here
Pablo Gallego (2017) On Runge-Kutta discontinuous Galerkin methods for compressible Euler equations and the ideal MHD model
Markus Zenk (2017) On Numerical Methods for Astrophysical Applications download here
Wasilij Barsukow (2018) Low Mach number finite volume methods for the acoustic and Euler equations download here
Marlies Pirner (2018) “Kinetic modeling of gas mixtures” download here
Jens Klotzky (2018) “Well-posedness of a fluid-particle interaction model” download here
Simon Markfelder (2020) "Convex integration applied to multi-dimensional compressible Euler equations" download here
Jonas Berberich (2020) "Fluids in Gravitational Fields – Well-Balanced Modifications for Astrophysical Finite-Volume Codes" download here
Andrea Thomann (2020) (jointly w. Gabriella Puppo) “Numerical methods for all-speed flows for the Euler equns. incl. well-balancing of source terms” download here
Marc Herrmann (2021) (jointly with Stephan Schmidt) "The total varisation on surfaces and of surfaces"
Farah Kanbar (2022) Asymptotic and Stationary Preserving Schemes for Kinetic and Hyperbolic Partial Differential Equations
Sandra Warnecke (2022) (jointly with Cory Hauck & Jeff Haack) Numerical schemes for multi-species BGK equations based on a variational procedure
Humboldt fellows
Yunguang Lu
Gui-Qiang Chen
Ujjwal Koley (2012 - 2014)
Yan Xu
Feng Xie
some former long term visitors and pos-docs
Nils-Henrik Risebro (Oslo) (April 23 - July 28, 2017)
Eduard Feireisl (Prague) (Oct. 1 - 31, 2016, Oct. 1 - 31, 2018)
Jiang Xu (Nanjing, China) (July 9 - 31)
Gabriella Puppo (Como, Italy) (Oct 12, 2015 - Feb. 6, 2016, Jan. 22 - Feb. 4, 2017, May 7 - 13, 2017)
Sibusiso Mabuza (former postdoc)
Nadine Even (postdoc until Dec. 2015)
Praveen Chandrashekar (Tata Institute of Fundamantal Research Centre of Applicable Math): April 28 - June 25, 2013, June 15 - July 22, 2014, April 3 - May 2, 2015, June 1 - July 31, 2016, July 5 - 16, 2017, April 8 - May 6, 2018, June 1 - 30, 2019
Feng Xie (Shanghai Jiao Tong Univ.): June 1 - Aug. 30, 2015
Rony Touma (Lebanese American University, Beirut): Oct. 2013 - Nov. 2013, Jan. 2014, July 2015
Yan Xu (University of Science and Technology of China, Hefei, China): Feb., March 2014, June - Aug. 2014
Yinhua Xia (University of Science and Technology of China, Hefei, China): Sept. 2013 - August 24, 2014
Sudarshan Kumar Kenettinkara (TIFR CAM in Bangalore): Jan. 1 - Feb 28, 2014
Ujjwal Koley May 14, 2011 - April 16, 2013. He now is at TIFR CAM in Bangalore
some of my current collaborators
Qin Li (Madison, Wisc., USA)
Walter Boscheri (Ferrara, Italy)
Seok-Bae Yun (Korea)
Christophe Chalons, Versaille University, France
Marlies Pirner, (Münster University, Germany)
Cory Hauck, Oak Ridge National Laboratory, USA
Min Tang Shanghai Jiao Tong University, China
Eduard Feireisl, Prague
Praveen Chandrashekar TIFR Bangalore
Yunguang Lu, Hangzhou Normal University
Nils-Henrik Risebro, Oslo
Fritz Röpke, Heidelberg
some of my former collaborators
Volker Springel, MPI Garching
Francois Bouchut, Université Paris-Est - Marne-la-Vallée
Pierre-Emmanuel Jabin, College Park, Maryland
Kenneth Karlsen, Oslo
Ujjwal Koley, TIFR Bangalore
Siddhartha Mishra, ETH
Jens Niemeyer, Göttingen
Wolfram Schmidt, Sternwarte Hamburg
Gui-Qiang Chen, Oxford
former post-docs
post-doc
Simon Markfelder heory of the multi-dimensional compressible Euler equations