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 ‘High-order upwind summation-by-parts methods for nonlinear conservation laws’ on arXiv 2023-11-27

New Preprint ‘Step size control for explicit relaxation Runge-Kutta methods preserving invariants’ on arXiv 2023-11-27

New Preprint ‘Multiderivative time integration methods preserving nonlinear functionals via relaxation’ on arXiv 2023-11-08

Summer school ‘Research Software Engineering with Julia: Basics, Visualization, and Statistics’ in Stuttgart 2023-10-08

New Paper ‘Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws’ published in ACM Transactions on Mathematical Software 2023-09-28