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I am an Assistant Professor in Applied Mathematics at the University of Hamburg. 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.

News

New Paper ‘Issues with positivity-preserving Patankar-type schemes’ published in Applied Numerical Mathematics 2022-08-10

New Paper ‘On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows’ published in Frontiers in Physics 2022-07-02

Talk ‘Efficient and robust step size control for computational fluid dynamics’ on 2022-05-11 2022-05-05

New Paper ‘A Note on Numerical Fluxes Conserving a Member of Harten’s One-Parameter Family of Entropies for the Compressible Euler Equations’ published in Journal of Computational Physics 2022-04-21

New Preprint ‘On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows’ on arXiv 2022-03-22