论文标题
一种未固定的有限元方法，具有直接扩展稳定，用于平滑域上的时间谐波麦克斯韦问题
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains
论文作者
论文摘要
我们提出了一种未限定的元素方法，用于在平滑域上数字求解时谐波麦克斯韦方程。模型问题涉及一个Lagrangian乘数，以放宽向量未知的差异约束。允许域的嵌入式边界任意切开背景网格。未实现的方案是基于混合内部惩罚表述，其中使用尼茨罚款方法来在弱意义上强制执行边界条件，并基于局部直接扩展运算符采用了惩罚稳定技术，以确保切割要素的稳定性。我们证明了INF-SUP稳定性，并获得了能源规范下的最佳收敛速率，以及矢量未知和Lagrangian乘法器的$ l^2 $ Narm。提出了两个和三个维度的数值示例，以说明该方法的准确性。
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The embedded boundary of the domain is allowed to cut through the background mesh arbitrarily. The unfitted scheme is based on a mixed interior penalty formulation, where Nitsche penalty method is applied to enforce the boundary condition in a weak sense, and a penalty stabilization technique is adopted based on a local direct extension operator to ensure the stability for cut elements. We prove the inf-sup stability and obtain optimal convergence rates under the energy norm and the $L^2$ norm for both the vector unknown and the Lagrangian multiplier. Numerical examples in both two and three dimensions are presented to illustrate the accuracy of the method.
