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Welcome to the homepage of the Numerical Analysis group!
Since February 2025, the Numerical Analysis group has been headed by Philipp Öffner. Its focus is on the development and analysis of numerical methods for solving ordinary and partial differential equations (ODEs/PDEs), in particular hyperbolic conservation equations. A central concern is the numerical treatment of non-linear conservation and balance equations, as they occur in numerous applications and for which no analytical solutions usually exist. The group develops and investigates efficient and stable numerical methods with regard to accuracy, stability and performance.
In addition to numerics, mathematical modeling also plays an important role, particularly in the context of fluid mechanics. The issues addressed originate from a wide range of scientific and technical application areas, including geophysics, environmental sciences and engineering.
Specifically, the members of the working group deal with the numerical solution of the Euler equations of gas dynamics, which are relevant in aerospace engineering, the wave equation for describing acoustic processes and the shallow water equations, as used in oceanography or in the modeling of river flows. The aim is to develop robust and efficient numerical methods that are both theoretically sound and practically applicable.