论文标题
时空不符合的有限元方法，用于移动域上的时期问题
Space-time unfitted finite element methods for time-dependent problems on moving domains
论文作者
论文摘要
我们提出了一个时空方案，该方案将空间中未实现的有限元方法与不连续的Galerkin时间离散化结合在一起，以实现移动域或接口的抛物线问题的准确数值近似。我们利用汇总的有限元空间来获得相对于切口的鲁棒性。在板上进行聚合以具有时空离散空间的张量产物结构，这在数值分析中是必需的。我们分析了所提出的算法，提供稳定性，条件号边界和各向异性\ emph {a先验}错误估计。一组数值实验证实了移动域上抛物线问题的理论结果。该方法适用于拓扑变化的传质问题。
We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We make use of an aggregated finite element space to attain robustness with respect to the cut locations. The aggregation is performed slab-wise to have a tensor product structure of the space-time discrete space, which is required in the numerical analysis. We analyse the proposed algorithm, providing stability, condition number bounds and anisotropic \emph{a priori} error estimates. A set of numerical experiments confirm the theoretical results for a parabolic problem on a moving domain. The method is applied for a mass transfer problem with changing topology.
