In the course of this project, reduced basis methods (RB) for parametrized nonlinear transport problems shall be developed. RB methods are a model reduction technique providing efficient, reduced models which allow fast parameter variations through an offline/online decomposition.
In the past, RB methods have been developed for stationary problems with finite element discretizations and linear evolution problems with finite volume discretizations. This project, in contrast, aims at the development of RB methods for time dependent problems especially including non-linear terms and more complex systems of partial differential equations. In particular, we consider scalar nonlinear convection-diffusion-reaction equations and systems with a further extension by an elliptic equation. A possible application for this concept, that we have in mind, is the 2-Phase flow in porous media.
The challenges of the project are firstly the non-linear character of the model equations and secondly, the design of efficient and rigorous a posteriori estimators. Those estimators and their efficient implementation are not only of interest for the validation of computed simulations. They can also play an important role during the offline phase, when the reduced basis is generated, by accelerating the selection of new base functions.
The project is funded by the "Deutsche Forschungsgemeinschaft" (DFG).
