The research priorities within the area of Analysis, Numerical Analysis and Optimization are numerous, and extend from analytical questions concerning partial differential equations to simulation and optimization. Among the topics are geometric problems, biomechanics, energy technology, fluid dynamics, the genesis of microstructures, and dynamic systems. In the past two years two excellent mathematicians have taken up professorships here: Professor Paola Pozzi and Professor Christoph Scheven. In the second funding period of DFG Priority Programme 1253 “Optimization with Partial Differential Equations”, the Faculty of Mathematics is represented with three projects conducted by the research groups of Professor Arnd Rösch and Professor Schultz, confirming its leading position in this area of research. The project topics are “Numerical analysis and discretization strategies for optimal control problems with singularities” (Professor Rösch jointly with Professor Thomas Apel and Professor Boris Vexler), “Multi-Scale Shape Optimization under Uncertainty” (Professor Schultz jointly with Professor Sergio Conti and Professor Martin Rumpf) and “Design and Analysis of Adaptive Finite Element Discretizations for Optimal Control Problems” (Professor Rösch jointly with Professor Kunibert Siebert).
An important area of application for the work of the research group of Professor Schultz on power network optimization is the optimization of gas transport in pipeline systems. Here the research group cooperates with the gas transmission company Open Grid Europe in Essen and is ­supported by the Bundesnetzagentur and the BMWi in investigating technical capacities in gas networks. In a project funded by Stiftung Mercator, Professor Schultz is working on ­“Resource-saving route planning in the Ruhr Metropolis using stochastic optimization” jointly with the group of Professor Uwe Clausen of TU Dortmund. He is a member of the new Research Training Group 1855/1 “Discrete Optimization of Technical Systems under Uncertainty” at TU Dortmund.
Professor Neff, Dirk Pauly and Professor Karl-Josef Witsch were together able to prove in a ­series of papers a far-reaching generalization of the Korn inequality, with applications to elastoplasticity and homogenization. This was achieved by combining techniques from elasticity theory with methods for Maxwell equations.
The research groups of Professors Ulrich ­Dierkes,  Andreas Gastel,  Frank Müller,  Pozzi and Scheven are working on partial ­differential equations motivated by geometric problems.
The number of participants makes it possible to study the topic in ample breadth, from differential geometry through analysis to numerical analysis, at the same time as maintaining a lively exchange of ideas.
Professor Petra Wittbold together with Professor Etienne Emmrich has successfully applied for funding of an institute partnership with the University of Warsaw on the subject of “Nonlinear differential equations: analysis, discretization methods, and applications”. The funding period began in January 2013 and will run until December 2015.
In the summer of 2012, a Humboldt scholarship for experienced scientists was granted to a Vietnamese postdoc. In the coming years, Bui Trong Kien will be a guest of the research group of Professor Rösch at the University of Duisburg-Essen for a total of 18 months.
The Mathematics and Computer Science ­research group (Professor Heiner Gonska) works in the border area between mathematics and computer science. The main focus is on Computer Aided Geometric Design, its historical and theoretical foundations in analysis, approximation theory, the theory of inequalities and of wavelets. The algorithms derived from this theory are similarly considered, in particular those for curves and surfaces, and signal and image processing. Spline methods play an important role here. Since 2005, the group has been the organizer of the research and teaching project “Center of ­Excellence for Applications of Mathematics” of the German Academic Exchange Service (DAAD). In addition to the University of Duisburg-Essen and the University of Wuppertal, 15 institutions in ten countries of South Eastern Europe are involved in this project.