Non-Newtonian Fluids

Non-Newtonian fluids appear in various applications including for example paints, medical liquids, gels, etc. The challenge is the non-linear and sometimes even non-explicit constitutive law that relates the extra stress tensor and the shear rate. For incompressible fluids in this framework we have investigated convergence of finite element approximations to the unsteady fluid motion. For this purpose tools from finite element theory such as local interpolation operators and Fortin operators are instrumental. Currently, we are also concerned with the numerical analysis of non-standard boundary conditions that occur, e.g., in polymer melts, and include slipping behaviour.