## Numerical methods for surface fluids

The project considers a class of surface Navier-Stokes equations which are used to model viscous two-dimensional incompressible fluidic surfaces. We restrict to sufficiently smooth closed oriented (evolving) surfaces embedded in $\mathbb{R}^3$ . The main topic of the project is the development of efficient and reliable finite element based numerical simulation methods for these surface Navier-Stokes equations. Such methods have been developed for stationary surfaces in the previous funding period and are now extended to evolving surfaces. Besides method development we also define benchmark problems and elaborate rigorous stability and error analyses. Finally, we also develop and investigate model extensions towards two-phase surface flows and active flows.