報告題目：An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains
報告人：謝小平 教授 （四川大學數學學院）
邀請人：沈曉芹 教授 （理學院數學係）
報告時間：2023年4月13日下午4:00-5:30
報告地點：教九樓理學院會議室9-320
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.
報告人簡介：謝小平，四川大學數學學院教授（博導），四川省學術和技術帶頭人，教育部新世紀優秀人才，德國洪堡學者。現兼任四川省普通本科高等學校數學類教學指導委員會秘書長,中國工業與應用數學學會油水資源數值方法專業委員會副主任委員，中國工業與應用數學學會高性能計算與數學軟件專業委員會委員，中國仿真學會集成微係統建模與仿真專業委員會委員。主要從事偏微分方程數值解相關領域的研究工作。曾獲教育部自然科學獎二等獎。
