Representative research projects

In the doctoral research projects we will combine in novel ways analytical, numerical, and modeling aspects related to energy/entropy functionals and their dissipation mechanisms. For example, we will combine analysis and modeling to begin a mathematical investigation of the GENERIC framework and develop new numerical methods that are inspired by analytical insights (relative entropy methods, curves of maximal slope) or modeling assumptions (maximum entropy production). The research projects are strategically located between the established research fields of the participating professors and will therefore require interaction and cooperation, bridging between different subdisciplines.

All doctoral researchers will be supervised jointly by two professors.

Project 04
Maximum entropy production for compressible Euler equations
Advisors: Michael Westdickenberg and Michael Herty
Keywords: Compressible Euler equations, entropy production, curves of maximal slope
Project 09
Asymptotic preserving schemes for control problems of kinetic differential equations
Advisors: Martin Frank and Michael Herty
Keywords: Asymptotic preserving methods, radiotherapy treatment planning, moment closure
Project 11
Relative entropy methods for asymptotic preserving IMEX schemes
Advisors: Sebastian Noelle and Michael Westdickenberg
Keywords: Stiff systems of conservation laws, asymptotic preserving IMEX schemes, relative entropy
Project 13
Numerical methods for bending energy minimization
Advisors: Heiko von der Mosel and Michael Herty
Keywords: Elastic knots, energy decay, smoothed penalization methods
Project 15
Entropic effects in stochastically perturbed PDE
Advisors: Maria Westdickenberg and Michael Herty
Keywords: Stochastic PDE, large deviations, nucleation, competition between energy and entropy
Project 16
Curves of maximal slope for curvature functionals
Advisors: Heiko von der Mosel and Michael Westdickenberg
Keywords: Integral Menger curvature, minimizing movements, Gamma convergence