报告题目：An unfitted finite element method by direct extension for elliptic problems on domains with curved boundaries and interfaces

报 告 人：谢小平教授（四川大学）

报告时间：2022年12月14日  14:30

报告地点：腾讯会议（314998708）

报告摘要：

We propose and analyze an unfitted finite element method of arbitrary order for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direet extension of the finite element space defined on interior elements, in the sense that there is no degree of freedom locating in boundary/interface elements. We apply a non-symmetric bilinear form and the boundary/jump conditions are imposed in a weak sense in the scheme. The method is shown to be stable without any mesh adjustment or any special stabilization. The optimal convergence rate under the energy norm is derived, and $O(h^ {-2} )$-upper bounds of the condition numbers are shown for the final linear systems. Numerical results in both two and three dimensions are presented to ilustrate the accuracy and the robustness of the method.

报告人简介：

谢小平，四川大学数学学院教授、博士生导师，国家级一流专业“信息与计算科学”专业负责人，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”，华为-四川大学数学联合实验室技术委员会委员，四川省专家评议委员，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。发表高水平论文80多篇。先后主持国家自然科学基金项目6项，承担国家973项目子课题1项。获2020年度教育部自然科学奖二等奖（排名1）。