论文标题
关于移动域的时间依赖的Stokes问题的未效量的有限元方法
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
论文作者
论文摘要
我们分析了一种欧拉有限元法，结合了使用CutFem方法和Inf-Sup稳定的Taylor-Hood Elements应用于时间依赖的Stokes方程的Eulerian时时间探索方案，以进行空间离散。这基于Lehrenfeld \＆Olshanskii提出的方法[ESAIM：M2AN 53（2）：585--614]在移动域的标量对流 - 扩散问题的背景下，并将其广泛用于Burman，Freman，Freei \＆Massing [Arxiv [Arxive]的非平稳性Stokes问题。该分析包括通过在离散CutFem设置中集成在近似级别集域上的几何误差。该方法已实现，并使用数值示例说明了理论结果。
We analyse a Eulerian Finite Element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations using the CutFEM approach with inf-sup stable Taylor-Hood elements for the spatial discretisation. This is based on the method introduced by Lehrenfeld \& Olshanskii [ESAIM: M2AN 53(2):585--614] in the context of a scalar convection-diffusion problems on moving domains, and extended to the non-stationary Stokes problem on moving domains by Burman, Frei \& Massing [arXiv:1910.03054 [math.NA]] using stabilised equal-order elements. The analysis includes the geometrical error made by integrating over approximated levelset domains in the discrete CutFEM setting. The method is implemented and the theoretical results are illustrated using numerical examples.
