报告题目 (Title)：An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains（光滑区域时谐Maxwell问题的一种直接延拓稳定非匹配有限元法）

报告人 (Speaker)： 谢小平 教授（四川大学）

报告时间 (Time)：2023年4月8日(周六) 10:00

报告地点 (Place)：腾讯会议（106-552-458，密码 230406）

邀请人(Inviter)：刘东杰 教授

主办部门：理学院数学系

报告摘要：

We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. 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 the 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 variables. Numerical examples in both two and three dimensions are presented to illustrate the accuracy of the method.