Druckansicht der Internetadresse:

Department of Mathematics

Chair of Applied Mathematics Prof. Dr. L. Grüne / Prof. Dr. A. Schiela

Print page

Set-valued numerical analysis

start of the project: 2008

funding institution:

until 2017: The Hermann Minkowski Center for Geometry in Tel Aviv, Israel;
DAAD; Bulgarian Academy of Sciences


principal investigator

AD Dr. Robert Baier

project members

Dr. Elza Farkhi

Dr. Gilbert Perria (project member until 09/2010  )


The project leader continues the project which was started 1995 by Prof. Dr. Frank Lempio.

Modelling of differential equations with discontinuous right-hand sides, dynamical systems with uncertainties, non-smooth optimization problems, and optimal control problems lead to differential equations with set-valued right-hand sides, so-called differential inclusions.

Within the research project "Set-Valued Numerical Analysis", differential inclusions are investigated qualitatively and quantitatively, and algorithms for their numerical solution are developed.

The numerical solution of such differential inclusions requires algorithms from set-valued numerical analysis, especially integration techniques for set-valued integrands and interpolation techniques for set-valued maps, based e.g. on set-valued finite element methods, set-valued divided differences and embeddings of convex compact sets. Especially, one focus is laid on the approximation of reachable sets at a given time which consist of all endpoints of admissible trajectories of a differential inclusion.

There are strong connections to the direcet discretization of optimal control problems, e.g. in questions on the (order of) convergence of the optimal control/trajectory of the discrete problems to the corresponding optimal control/trajectory of the continuous problem.


The project members organized the following minisymposia and sessions on set-valued numerics.


responsible for the content: Lars Grüne

Facebook Twitter Youtube-Kanal Instagram Blog UBT-A Contact