90 min sessions on 25.01, 27.01, 01.02, 03.01, 08.02, and 10.02.2021
This short course is an online workshop
This short course is organized by SFB 1313.
Members and associated international members of SFB 1313, IRTG DROPIT and SimTech are invited to attend the short course. Participants will get 3 credits for attending the course.
For registering to the short course, please send an email to firstname.lastname@example.org.
Please add the following information:
- Last name
- First name
- SFB research projekt (if applicable)
The Stokes system and the Darcy system are the paradigms for laminar flows and flows in porous media, respectively. Mixed Finite Element (FEM) discretizations provide flux approximations with local mass conservation, of importance in the context of general multicomponent reactive flow and transport models. Unfortunately, these FEM are not coercive anymore, requiring a new tool for (order of) convergence investigations. We will develop this basis and discuss the most common finite elements (Taylor-Hood, Raviart-Thomas…). If time permits, we will also discuss the time-dependent case and in addition FEM for convection-dominated parabolic problem (streamline diffusion SUPG,…). The lectures are based on some new sections in the upcoming strongly enlarged new edition of Knabner, Angermann, "Numerical Methods for Elliptic and Parabolic Partial Differential Equations". The text will be provided to the participants.
Prof. Dr. Peter Knabner works in the field of Applied Analysis and Numerical Mathematics. After his Abitur in 1972, he studied mathematics at the Free University of Berlin and computer science at the Technical University of Berlin. After his diploma, he dealt for example with free boundary value problems and received his doctorate in 1983 at the University of Augsburg. There he habilitated in 1988 on mathematical models for transport and sorption of dissolved substances in porous media. Since 1994 he holds the chair of applied mathematics at the Friedrich-Alexander University Erlangen-Nürnberg.
Since the 1980s he has concentrated on the derivation, analysis and numerical approximation of mathematical models for flow and transport in porous media, with the aim of contributing to mathematics as well as to the concerned applications in engineering and natural sciences, in particular hydrogeology. The spectrum meanwhile extends to multiphase multicomponent flows, with vanishing/developing phases, general chemical reactions and effects of evolving microstructure on porous media flow.