Many materials of biomedical and engineering interest can be accurately modelled as generalised Newtonian fluids, that is, with an apparent viscosity depending locally on the flow field. Although these models may appear simple, their simulation imposes various challenges ranging from basic aspects such as boundary conditions, to more technical ones involving solver accuracy and efficiency. This work presents advanced finite element methods for the accurate, efficient, reliable simulation of incompressible flows involving generalised Newtonian fluids – a class which also includes the Newtonian case. Within that field, our scope is rather broad, addressing topics that go from enforcing boundary conditions to eliminating numerical artifacts; from flow simulations to inverse problems; from efficient time-stepping to space-time solvers; from stable to stabilised finiteelement methods. Our work is application-motivated, yet technique-driven: we have practical biomedical and engineering challenges as main motivation, but our focus lies on developing advanced numerical methods. Nonetheless, most of our techniques are immediately applicable not only to patient-specific simulations, but also to industrially relevant problems where complex Newtonian and non-Newtonian flows often feature.weiterlesen