报告题目：An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains
报告人：谢小平 教授 （四川大学数学学院）
邀请人：沈晓芹 教授 （hbs02红宝石线路数学系）
报告时间：2023年4月13日下午4:00-5:30
报告地点：教九楼hbs02红宝石线路会议室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.
报告人简介：谢小平，四川大学数学学院教授（博导），四川省学术和技术带头人，教育部新世纪优秀人才，德国洪堡学者。现兼任四川省普通本科高等学校数学类教学指导委员会秘书长,中国工业与应用数学学会油水资源数值方法专业委员会副主任委员，中国工业与应用数学学会高性能计算与数学软件专业委员会委员，中国仿真学会集成微系统建模与仿真专业委员会委员。主要从事偏微分方程数值解相关领域的研究工作。曾获教育部自然科学奖二等奖。
