This PhD project is about the development of structure preserving (e.g. mass and total energy) finite element discretizations of flow models in Geophy

. It intends to develop in a systematic manner by combining compatible finite
element (exterior calculus) with variational methods and by developing new basis functions that are constructed via the method of subdivision adaptive structure preserving schemes. As such, the topic is of high interest particularly in the GFD community, because there is a constant need of improving both accuracy and efficiency of fluid solvers. Here, mesh
adaptivity plays a crucial role as it permits to more accurately resolve local features of interest while keeping the resolution course elsewhere, keeping the computational cost affordable. While mesh adaptivity has been successfully implemented in various flavours, there is still a lack of adaptivity methods that preserve important structures of the underlying dynamical
system. This is important to improve the reliability and accuracy of the numerical simulations that are the essence of weather and climate predictions.