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

。它旨在通过将相容有限元(外部微积分)与变分方法相结合并开发新的基函数来系统地发展，这些基函数是由细分自适应结构保持格式构造的。因此，这一主题引起了人们的高度兴趣，特别是在GFD社区，因为不断需要提高流体解算器的精度和效率。在这里，网格自适应起着至关重要的作用，因为它允许更准确地解析感兴趣的局部特征，同时保持其他地方的解析过程，使计算成本保持在可承受的范围内。虽然网格自适应已经以各种形式被成功地实现，但仍然缺乏保存底层动态系统的重要结构的自适应方法。这对于提高数值模拟的可靠性和准确性很重要，数值模拟是天气和气候预测的本质。

. It intends to develop in a systematic manner by combining compatible finiteelement (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 dynamicalsystem. This is important to improve the reliability and accuracy of the numerical simulations that are the essence of weather and climate predictions.