Welcome to the homepage of the Numerical Analysis Research Group!

Since February 2025, Philipp Öffner has led the Numerical Analysis group, which focuses on the development and analysis of numerical methods for ordinary and partial differential equations (ODEs/PDEs), particularly hyperbolic conservation laws. A key area of interest is the numerical solution of nonlinear conservation and balance laws, which arise in various applications and lack analytical solutions. The group specializes in constructing novel methods, analyzing, and optimizing efficient and stable numerical schemes.

Beyond the development of structure preserving methods, mathematical modeling plays another crucial role, in particular in fluid mechanics. The group investigates problems from diverse scientific and technical fields, including geophysics, environmental sciences, and engineering.

Specifically, the team works on the numerical approximation of the Euler equations of gas dynamics, relevant to aerospace engineering, the wave equation, which describes acoustic phenomena, and the shallow water equations, used in geophysical applications such as river currents and oceanography. Their goal is to develop robust and efficient numerical methods that are both theoretically rigorous and practically applicable.