报告题目：A Class of Stabilized Nonconforming Finite Element Methods for Fourth-Order PDEs on Surfaces

报告人：吴朔男，北京大学

报告时间：7月1日  下午3:30

报告地点：管理楼1218

摘要：

This talk presents the development and analysis of stabilized nonconforming finite element methods for fourth-order surface PDEs, focusing on the surface biharmonic problem and the stream-function formulation of the surface Stokes problem.

First, we introduce a surface New-Zienkiewicz-type (NZT) element for the biharmonic equation. By employing the Piola transform to connect vertex gradients across adjacent elements , the discrete space achieves H^1-relative conformity and weak H(div) conformity. This structure allows for a parameter-free stabilization, yielding optimal error estimates under low regularity assumptions.

Second, we discuss a stabilized Morley finite element method for the surface Stokes problem. To overcome the geometric consistency challenges inherent in polyhedral surface approximations, a novel geometric analysis framework is introduced. This approach successfully establishes optimal error estimates in various norms, demonstrating the robustness of the intrinsic nonconforming scheme.

个人简介：

吴朔男分别于2009年和2014年在北京大学数学科学学院获得学士和博士学位，2014年至2018年在美国宾州州立大学进行博士后研究，2018年加入北京大学数学科学学院信息与计算科学系，现任长聘副教授/研究员。主要研究方向为偏微分方程数值解，研究内容包括：磁流体力学中的磁对流的稳定离散、非线性、高阶椭圆型方程的非协调有限元的构造和分析，空间分数阶问题的离散和快速求解器，曲面有限元方法等。获基金委优秀青年科学基金(2022)、第六届中国工业与应用数学学会应用数学青年科技奖(2022)。