报告人 ：谢小平（四川大学）

时间：2023年04月28日 16:30--

地址：理科楼LA106

摘要：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.

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，在SIAM J. Control Optim.、SIAM J. Numer. Anal.、Numer. Math.、Comput. Methods Appl. Mech. Engrg等期刊发表论文90多篇。曾获教育部自然科学奖二等奖。

邀请人：王坤

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