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

Lisa Lechner                        a structure-preserving compact high-order method for multi-dim. hyperbolic conservation laws: the generalized Active Flux method

Jayesh Badwaik                   moving mesh method in two space dimensions for the Euler equations - uncertainty quantification for conservation laws

current Master-thesis students

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

Janina Kern                      on the generalized Active Flux method - analysis und numerics

Armin Hofmann                a neural network as a troubled-cell indicator in the numerical simulations of conservation laws

Andrea Lörke                    on numerics for the compressible Euler equations

Annika Gutzeit                  low Mach and well-balanced num. methods for Euler w. gravity using relaxation Riemann solvers

Melissa Lange                  inverse problems in a Baysian setting

current Bachelor-thesis students

Simon Krotsch                   theory of conservation laws in one space dimensions

Leon Jakobi                       shallow water equations and numerical applications using CLAWPACK

some former Master-thesis students

Amelie Gehring                 Linear Landau Damping Coupled with Relaxation for the Two-Species Vlasov-Poisson-BGK System

Luis Kaiser                        Fast, Accurate, and Scalable Numerical Wave Propagation: Enhancement by Deep Learning

Yu-Chen Cheng                A well-balanced method for an unstaggeed central scheme (applied to Euler with gravity)

Veronika Mayerhofer        Simulating Water Waves in Networks Using a High-Order Accurate Entropy Stable Finite Volume Scheme  

Moritz Beck                      Online Lernalgorithmen als Rekonstruktionsmethode in der optischen Tomographie    

Kaja Jurak                        Multiscale Analysis and Ill Conditioning in the Diffusive Limit of the Inverse Problem for Chemotaxis in the Bayesian Setting

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

Theresa 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 coupled with relaxation for the Vlasov-Poisson-BGK equation

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            On the uniqueness of solutions to the two-dimensional 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

Sophie Lauer               The low Mach limit of the compressible Navier-Stokes equations

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 Euler gleichungen)

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 termsdownload 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

Claudius Birke    (2024)     Low Mach and Well-balanced Numerical Methods for Compressible Euler and Ideal MHD Equations with Gravity

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

Marlies Pirner

Stephan Schmidt

Markus Zenk

Sibu Mabuzza

Ujjwal Koley

Nadine Even


Simon Markfelder               theory of the multi-dimensional compressible Euler equations

Junming Duan                     numerical methods for hyperbolic conservation laws  (Humboldt Fellow Oct. 2023 - Sept. 2025)

guest professor

Yunguang Lu                      theory of conservation laws, compensated compactness