Model hierarchies and higher-order discretisation of time-dependent thin-film free boundary problems with dynamic contact angle

We present a mathematical and numerical framework for thin-film fluid flows over planar surfaces including dynamic contact angles. In particular, we provide algorithmic details an implementation of higher-order spatial temporal discretisation the underlying free boundary problem using finite element method. The corresponding partial differential equation is based on thermodynamically consistent energetic variational formulation energy viscous dissipation in bulk, surface, at moving line. Model hierarchies limits strong weak line are established, implemented studied. analyze performance algorithm investigate impact angle evolution two benchmark problems: gravity-driven sliding droplets instability ridge.