Multi-scale modeling

If a mathematical model contains many different scales the computational cost for its numerical solution is very large. The smallest scale must be resolved over the distance of the largest scale. A huge number of unknowns are required and until recently many such problems could not be treated computationally. We will discuss a new set of numerical techniques that couples models for different scales in the same simulation in order to handle many realistic multi-scale problems. In most of this presentation we shall survey existing methods but we shall also give some new observations.