Stephan Dahlke

Research Area

The main field of research is the development and the analysis of efficient numerical algorithms for operator equations. Realistic problems, e.g., in 3D, usually give rise to systems with a huge number of degrees of freedom, so that adaptive strategies are necessary to increase efficiency. We are particularly interested in adaptive schemes that are based on quite recently developed new basis functions, the so-called wavelets. The strong analytical properties of wavelets can be used to design adaptive refinement strategies that are guaranteed to converge with optimal order for a large class of problems. Moreover, we work on the mathematical modelling and numerical simulation of microbiological systems.

Expertise

Numerical Analysis
Wavelets
Theory of PDEs
Frames and Coorbit Theory
Function Spaces
Mathematical Modelling of Biological Systems

Recent Publications, Last 3 Years

1. Dahlke S, Schneider C (2019) Besov regularity of parabolic and hyperbolic PDEs, Analysis and Applications 17(2), 235-291, DOI 10.1142/S0219530518500306.

2. Dahlke S, De Mari F, De Vito E, Sawatzki L, Steidl G, Teschke G, Voigtlaender F (2018) On the atomic decomposition of coorbit spaces with non-integrable kernel. In: Landscapes of Time-Frequency Analysis, (H.-G. Feichtinger, P. Boggiatto, E. Cordero, M. de Gosson, F. Nicola, A. Oliaro, A. Tabacco, eds.), Birkhäuser, 75-144.

3. Dahlke S, Hansen M, Schneider C, Sickel W (2020) On Besov regularity of solutions to nonlinear elliptic partial differential equations. Nonlinear Analysis 192, 111686, https://doi.org/10.1016/j.na.2019.111686.

http://www.mathematik.uni-marburg.de/~dahlke