标题： 切割有限元外微积分的鬼影稳定化 显示英文标题

标题： Ghost stabilisation for cut finite element exterior calculus

摘要： 我们通过在有限元外微积分的语言中引入切割有限元方法，提出一种稳定化方法——针对任何形式次数——使该方法在界面相对于网格的位置方面具有鲁棒性。 我们证明，在物理域上增加这种稳定化后的$L^2$-范数与包含所有有限元空间自由度（包括物理域外部的自由度）的“活动”网格上的$L^2$-范数是统一等价的。 我们展示了如何将此CutFEEC方法应用于在非匹配网格上离散任意维度和拓扑的霍奇拉普拉斯方程。 提供了一个数值示例，涉及在一个填充环面之上定义的符合有限元空间$H^{\text{curl}}$，其收敛性和条件数缩放与边界相对于背景网格的位置无关。 显示英文摘要

摘要： We introduce the cut finite element method in the language of finite element exterior calculus, by formulating a stabilisation -- for any form degree -- that makes the method robust with respect to the position of the interface relative to the mesh. We prove that the $L^2$-norm on the physical domain augmented with this stabilisation is uniformly equivalent to the $L^2$-norm on the ``active'' mesh that contains all the degrees of freedom of the finite element space (including those external to the physical domain). We show how this CutFEEC method can be applied to discretize the Hodge Laplace equations on an unfitted mesh, in any dimension and any topology. A numerical illustration is provided involving a conforming finite element space of $H^{\text{curl}}$ posed on a filled torus, with convergence and condition number scaling independent of the position of the boundary with respect to the background mesh.