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

.它打算发展在一个系统的方式相结合的兼容finiteelement（外部微积分）与变分方法，并通过开发新的基函数，通过细分自适应结构保持计划的方法构建。因此，该主题特别是在GFD社区中具有很高的兴趣，因为不断需要提高流体求解器的精度和效率。在这里，网格自适应性起着至关重要的作用，因为它允许更准确地解决感兴趣的局部特征，同时保持其他地方的分辨率过程，保持计算成本负担得起。虽然网格自适应已经成功地实现了各种风味，仍然缺乏自适应方法，保留底层dynamicalsystem的重要结构。这对于提高作为天气和气候预测本质的数值模拟的可靠性和准确性非常重要。

. 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.