Numerical Analysis
As Numerical Analysis and Scientific Computing group we work on numerical methods, mainly for partial differential equations. We are happy about your interest, feel free to contact us!
On the research level we develop efficient and robust numerical schemes, for example by means of structure preservation. For such schemes we deal with convergence analysis and both a priori and a posteriori error estimates. In situations of uncertain data we investigate techniques for uncertainty quantification and data assimilation that can be incorporated in numerical schemes. Efficiency can be enhanced by model order reduction as well as adaptivity, both on the level of the model and on the level of the mesh.
Most partial differential equations we work on are coming from compressible fluid dynamics. Applications include for example gas networks, compressible Euler equations and non-Newtonian fluids. Also partial differential equations from other fields such as electrodynamics, geothermics, medicine and biology are considered.
On the other hand for teaching we offer a wide range of courses for students on various aspects of numerical approximation. Notably, we aim for a solid basic education that will be practical and useful for anyone. Building on that, we enjoy offering specialisation in areas with close connections to our research.
2024/05/02,
14:00-15:00
Vortrag im AG Numerik Seminar, M.Sc. Kiwoong Kwon, TUD, AG Numerik
A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model
The Keller-Segel model is a fundamental mathematical model used to describe the movement of biological cells (like bacteria or amoebas) in response to chemical signals in their environment. This phe…
2024/05/08,
17:15-19:00
Vertex Algebras in Number Theory, Geometry and Physics
Mathematisches Kolloquium im Sommersemester 2024
Dr. Sven Möller, TU Hamburg / TU Darmstadt Vertex algebras describe 2-dimensional conformal field theories in physics. They were introduced in the 1980s to explain mysterious connections betwe…
2024/05/15,
17:15-19:00
Integer optimization in pseudopolynomial time and beyond: For all - there exist statements
Mathematisches Kolloquium im Sommersemester 2024
Prof. Dr. Robert Weismantel, ETZ Zürich A classical result of Papadimitriou from 1982 states that integer optimization problems in standard form can be solved in running time max{||b||_\infty,…
2024/05/22,
17:15-19:00
Can primitive chemotaxis generate spatial structures?
Mathematisches Kolloquium im Sommersemester 2024
Prof. Dr. Michael Winkler, Universität Paderborn The collective behavior in populations of single-cell species described by parabolic models is considered. A predominant emphasis will be on ca…
2024/06/05,
15:15-19:00
Moduli spaces in the Langlands program
Mathematisches Kolloquium im Sommersemester 2024
Prof. Dr. Eva Viehmann, Universität Münster The Langland program is a class of long-range conjectural relations between algebraic number theory and representation theory. For their realiz…