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：2022年12月9日下午14:00-16:00
腾讯会议ID: 591 542 260
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 direct 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 illustrate 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。
