Christian Klingenberg

research interests:

Mathematical Fluid Mechanics

    theory of hyperbolic conservation laws

      •   towards a proper solution concept for the multi-dim. compressible Euler equations

      •   convex integration, non-uniqueness for the multi-dim. compressible Euler equations

    structure preserving numerical schemes for Euler and ideal magnetohydrodynamics

      •   well-balanced and low Mach schemes for Euler equations with gravity

      •   genuinely multi-dim. schemes

      •   structure-preserving compact high-order method method

    applications in astrophysics

      •   numerical schemes for evolving stellar structure and evolution

      •   simulations of the evolution of the universe including magnetic fields

    kinetic equations and plasma, theory & numerics

      •   multi-species models, existence and qualitative behavior

      •   numerical schemes for multi-species BGK equations based on a variational procedure

    PDE inverse problems, kinetic models in biology with coefficients determined by experimental data

      •   theory: proving that it is possible to solve certain kinetic PDE inverse problems

      •   numerics: schemes that determine the coefficients from given experimental data

see also here

Our logo, showing the interplay between astrophysics (Cassiopeia) and fluid mechanics.

designed together with Sebastian Ohlmann

former workshops, conferences etc.:

       - Seminar series from Sept. 2020 - May 2022 Hyperbolic equations: Structure preserving numerical methods and other topics, see here

       - Oberwolfach workshop "Structure preserving numerical methods for hyperbolic equations", April 11 - 15, 2022 see here

       - Oberwolfach workshop "Modelling phenomena from nature by hyperbolci conservation laws", April 11, 17, 2021 see here

       - Fall school Oct. 1 - 5, 2018 in Würzburg: Hyperbolic conservation laws and mathematics of fluid mechanics, with lectures by   Constantine Dafermos, Eduard Feireisl, Sara Daneri and Simon Markfelder

       - 16th International Conference on Hyperbolic Problems, organized by M. Westdickenberg and myself Aug. 1 - 5, 2016.

       - Workshop in Würzburg, June 30 - July 3, 2015,Evolutionary Equations, theory & numerics”, see here

Dept. of Mathematics

Würzburg University

Emil Fischer Str. 40

97074 Würzburg


I am in room 03.011 (top floor)

phone: (0049) (0)931 318 5045

email:    christian.klingenberg (at)

upcoming visitors:

- Praveen Chandrashkar (Bangalore, India),  May 15 - June 1, 2024