Prof. Dr. Barbara Wohlmuth (TU München ) Interfaces, corners and point sources
Thursday, 28.11.2013 16:30 im Raum M5
In many multi-physics applications, coupled models and dimension-
reduced PDE systems play an important role in the mathematical
modelling of physical effects on different scales, e.g., fractures of co-
dimension 1 in porous media systems, networks of co-dimension 2 or
point sources. Although these simplified models seem very attractive
from the computational point of view, for coupled problems they may
result in a solution of reduced regularity. Mathematically, transmission
problems with piecewise smooth solutions or PDEs in a distributional
sense with singular solutions arise.
The global accuracy is often dominated by local effects at the inter-
faces, and local singularities can pollute the numerical solution. Here
we discuss several issues such as hierarchical limiting techniques, local
energy corrections and optimal estimates for the flux variables. The
coupling is controlled by pairs of balance equations providing a very
flexible framework. But stability and accuracy do not come for free.
Different examples illustrate the abstract concepts, special focus is on
surface based coupling techniques and highly non-linear dimension
reduced transport systems.