论文标题
使用离散扩展名的cutfem的cutfem显式踏入波程
Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension
论文作者
论文摘要
在本说明中，我们为波方程开发了一种完全明确的剪切有限元方法。该方法基于使用标准的Leap Frog方案与扩展运算符相结合，该扩展运算符在域内的节点值方面定义了域外部的节点值。我们表明，与扩展有限元空间相关的质量矩阵可能会导致完全显式的方案。我们得出该方法的稳定性估计，并提供最佳顺序估计。最后，我们提出了一些说明的数字示例。
In this note we develop a fully explicit cut finite element method for the wave equation. The method is based on using a standard leap frog scheme combined with an extension operator that defines the nodal values outside of the domain in terms of the nodal values inside the domain. We show that the mass matrix associated with the extended finite element space can be lumped leading to a fully explicit scheme. We derive stability estimates for the method and provide optimal order a priori error estimates. Finally, we present some illustrating numerical examples.
