We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preu{\ss} (SIAM J. Sci. Comput. 45(2), 2023, B139 - B165) for the bulk case with a method suggested by Sass, Reusken (Comput. Math. Appl. 146(15), 2023, 253-270) for the surface case. The geometry is allowed to change with time, and the higher order discrete approximation of this geometry is ensured by a time-dependent isoparametric mapping. The space-time discretisation approach allows for straightforward handling of arbitrary high orders. In that way, we also generalise results of Hansbo, Larson, Zahedi (Comput. Methods Appl. Mech. Engrg. 307, 2016, 96-116) to higher orders. The convergence of the proposed higher order discretisations is confirmed numerically.

翻译：我们针对耦合体-表域上的对流-扩散问题，提出了一种高阶时空非拟合有限元方法。该方法将Heimann、Lehrenfeld、Preuß（SIAM J. Sci. Comput. 45(2), 2023, B139-B165）提出的体域方法与Sass、Reusken（Comput. Math. Appl. 146(15), 2023, 253-270）提出的表域方法相结合。几何结构允许随时间变化，并通过时间依赖的等参映射保证几何的高阶离散近似。该时空离散化方法可简洁地处理任意高阶精度，从而将Hansbo、Larson、Zahedi（Comput. Methods Appl. Mech. Engrg. 307, 2016, 96-116）的研究成果推广至高阶情形。数值实验验证了所提出高阶离散格式的收敛性。