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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.
News
New Paper ‘Resolving Entropy Growth from Iterative Methods’ published in BIT Numerical Mathematics 2023-09-15
New Preprint ‘Stability of step size control based on a posteriori error estimates’ on arXiv 2023-07-25