Jan Giesselmann

• Hyperbolic conservation laws
• Compressible fluid flows
• Discontinuous Galerkin Methods
• A-priori and a-posteriori error estimates
• Model-adaptation
• Uncertainty quantification
• Observer-based data assimilation

Sommersemester 2026

• Efficient methods for data assimilation
• BSc Seminar

These are examples of thesis topics that I would be happy to supervise. If you are interested in any of these topics please send me an email. The topic will be made precise once we have discussed your scientific background and interests. If you are interested in different topic in numerical mathematics that is also possible,

BSc

• Structure preserving DG-in-time scheme for gradient flows
• Structure preserving DG-in-time schemes for Hamiltonian systems
• Error estimators for DG-in-time schemes
• Error estimators for CG-in-time schemes

MSc

• A posteriori error estimates for mixed finite elements for wave equations
• A posteriori error estimates for finite volume schemes for the heat equation
• A priori error estimates for a finite volume scheme for the Keller-Segel system
• A posteriori error estimates for moment approximations of kinetic equations
• A posteriori estimates for convection diffusion equations
• A high order energy consistent scheme for a phase field fracture model
• Operator learning for hyperbolic conservation laws

Other areas of my expertise where I would be happy to supervise theses are

• Discontinuous Galerkin schemes
• hyperbolic conservation laws
• a-priori and a-posteriori error estimators
• compressible multiphase flows

please contact me if you are interested in one of those.

Observer-based data assimilation for time-dependent flows in gas networks (Subproject C05 in SFB-TRR154 funded by German Research Foundation – DFG). This is a joint project with Martin Gugat, FAU Erlangen-Nuremberg.

A posteriori error control for statistical solutions of barotropic Navier-Stokes equations. Project in DFG SPP-2410 jointly with S. Krumscheid (KIT).

Dissipative solutions for the Navier-Stokes-Korteweg system and their numerical treatment. Project in DFG SPP-2410 jointly with Ph. Öffner (TU Clausthal).

I regularly receive unsolicited applications for research positions (PhD, postdoc, visiting scholar). While I appreciate genuine interest, I cannot respond to all messages individually. Applications are considered only if they show clear, personal engagement with my research.

If you wish to be taken seriously, please make sure your message demonstrates that you have read and understood my work. In particular:

• Refer to one of my recent publications by title, and explain briefly (2–3 sentences) what aspect of it connects to your own background or interests.
• Identify a specific problem, question, or result from my research that you would be interested in exploring further, and state why.

Your email should be concise, written in your own words, and accompanied by:

• A short CV (maximum two pages)
• If applicable, a brief research proposal or summary of previous work (maximum one page + literature)
• A statement on how you plan to fund your stay, or whether you are applying for a funded position (note: such positions are rarely available unless explicitly advertised).

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Thank you for your understanding.

I was co-leader of working group 5 “numerical methods and applications” of COST Action CA18232 – Mathematical models for interacting dynamics on networks from 2022 to 2024.

Some conference videos:

• ICERM Workshop Advances in PDEs: Theory, Computation and Application to CFD (Videos unten auf der Seite)
• CIRM-SMF Week on Inhomogeneous Flows

Dynamical, spatially heterogeneous model adaptation in compressible flows (funded by German research foundation (DFG))

Numerical methods for multi-phase flows with strongly varying Mach numbers Elite-program for Postdocs of Baden-Wuerttemberg Stiftung

Mathematical modeling of compressible fluids – from wild solutions to data integration – Research Seed Capital of University of Stuttgart and Ministry of Science, Research and Art Baden-Württemberg