The numerical treatment of the evolutionary incompressible Navier-Stokes equations, which determine many practicaIly relevant fluid flows, is an area of considerable interest for industrial as weIl as scientific applications. Im portant for drawing furt her conclusions for the behavior of certain flows in diverse disciplines such as (astro-)physics, engineering, meteorology, oceanog raphy, or biology is a reliable, robust and efficient numerical model. The goal of computing highly complex flows requires the development of sophisticated algorithms. In general, numerical schemes which do not...

In this work, we study numerical issues related to a common mathematical model which describes ferromagnetic materials, both in a stationary and non stationary context. Electromagnetic effects are accounted for in an extended model to study nonstationary magneto-electronics. The last part deals with the numerical analysis of the commonly used Ericksen-Leslie model to study the fluid flow of nematic liquid crystals which find applications in display technologies, for example. All these mathematical models to describe different microstructural phe nomena share common features like (i) strong...