论文标题
分析隐式扩展的曲柄 - 尼科尔森方案，用于在时间依赖域上的热方程
Analysis of an implicitly extended Crank-Nicolson scheme for the heat equation on a time-dependent domain
论文作者
论文摘要
我们考虑了曲柄 - 尼科尔森类型的时间步变方案，用于在欧拉坐标中移动域上的热方程。由于空间域在后续时间步长之间变化，因此需要从上一个时间步的扩展解决方案。遵循Lehrenfeld \＆Olskanskii [Esaim：M2an，53（2）：\，585-614，2019]，我们应用了一个基于所谓的幽灵式术语的隐式分机。对于空间离散，使用了剪切的有限元方法。我们在空间和时间上得出完整的先验错误分析，该分析在抛物线CFL条件下特别显示了时间和时间的二阶收敛。最后，我们在两个和三个空间维度中介绍了数值结果，这些结果确认了分析估计，即使在更大的时间步骤中也是如此。
We consider a time-stepping scheme of Crank-Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step is required. Following Lehrenfeld \& Olskanskii [ESAIM: M2AN, 53(2):\,585-614, 2019], we apply an implicit extension based on so-called ghost-penalty terms. For spatial discretisation, a cut finite element method is used. We derive a complete a priori error analysis in space and time, which shows in particular second-order convergence in time under a parabolic CFL condition. Finally, we present numerical results in two and three space dimensions that confirm the analytical estimates, even for much larger time steps.
