A stabilized nonconforming finite element method for the surface biharmonic problem；A posteriori error estimates by preconditioning

报告时间：2025年5月9日下午14:00-16：00

报告地点：红瓦楼826

报告题目一: A stabilized nonconforming finite element method for the surface biharmonic problem

报告人：吴朔男  副教授/研究员  北京大学 数学科学学院

报告内容简介：This talk presents a novel stabilized nonconforming finite element method for solving the surface biharmonic problem. The method extends the New-Zienkiewicz-type (NZT) element to polyhedral (approximated) surfaces by employing the Piola transform to define the connection of vertex gradients between adjacent elements. Key features of the surface NZT finite element space include its H¹-relative conformity and the weak H(div) conformity of the surface gradient, allowing for stabilization without the need for artificial parameters. Assuming that the exact solution and the dual problem possess only H³ regularity, we establish optimal error estimates in the energy norm and provide, for the first time, a detailed analysis yielding optimal second-order convergence in the broken H¹ norm. Numerical experiments are provided to support the theoretical results, and they suggest that the stabilization term may not be necessary.

报告人简介：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等。研究工作发表在Math. Comp., Numer. Math., SIAM J. Numer. Anal.等核心期刊上。曾获第六届中国工业与应用数学学会应用数学青年科技奖(2022)。

报告题目二: A posteriori error estimates by preconditioning

报告人：李雨文  研究员  浙江大学 数学科学学院

报告内容简介：In this talk, we present a framework that relates preconditioning with a posteriori error estimates in finite element methods. With the help of standard tools in auxiliary space preconditioning, we obtain classical two-sided error estimators of finite element methods for H(grad), H(curl), H(div) problems as well as new parameter-robust error estimators for H(curl) and H(div) problems. The material of the talk is based on joint work with Ludmil Zikatanov.

报告人简介：李雨文在南京大学取得本科和硕士学位，在加州大学圣迭戈分校获得数学博士学位。2019-2022年他在宾州州立大学担任研究助理教授，于2022年8月加入浙江大学数学科学学院担任百人计划研究员。他的主要研究方向是微分方程数值解，包括有限元方法、保结构方法、模型降阶等，研究发表于SINUM, MathComp, FoCM等计算数学核心期刊。

报告邀请人：黄学海