I am a Professor in Numerical Mathematics at Johannes Gutenberg University Mainz. My research is focused on the analysis and development of numerical methods for partial and ordinary differential equations. In particular, I am interested in the stability of these schemes as well as mimetic and structure-preserving techniques, allowing the transfer of results from the continuous level to the discrete one.

Research Interests

  • Numerical Analysis
    • Numerical schemes for hyperbolic balance laws and dispersive-dissipative equations: Discontinuous Galerkin methods, continuous and discontinuous spectral element methods, finite difference schemes, flux reconstruction, finite volume methods
    • Structure-preserving methods: Conservation/dissipation of entropy/energy, summation by parts operators, (skew-symmetric) splitting techniques, mimetic properties, filtering, artificial dissipation
    • Runge-Kutta methods, stability of time integration schemes
    • Adaptivity in time and space
    • Data-driven approaches combining analysis and data
    • Uncertainty quantification
  • Scientific Computing
    • Compressible Euler equations, shallow water equations, magnetic induction equation, numerical plasma physics, magnetohydrodynamics, dispersive wave equations
    • Multi-physics problems and astrophysical applications
    • Modeling and analysis of physical processes
    • High-performance computing (HPC) in Julia
    • Heterogeneous computing on CPUs and GPUs using OpenCL
    • Open source projects such as Trixi.jl, SummationByPartsOperators.jl, OrdinaryDiffEq.jl, NodePy, RK-Opt

Please find more information about our research in the section Research.

CV and members of the research group

Please find more information about us in the section People.


New Preprint ‘Structure-Preserving Numerical Methods for Fokker-Planck Equations’ on arXiv 2024-04-12

New Preprint ‘Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations’ on arXiv 2024-02-27

Talk ‘Structure-preserving numerical methods for nonlinear dispersive wave equations’ on 2024-02-15 2024-02-14

Julia User Group in Mainz (Germany) 2023-12-15

New Preprint ‘Using Bayesian Optimization to Design Time Step Size Controllers with Application to Modified Patankar-Runge-Kutta Methods’ on arXiv 2023-12-05