题目：Upwind Finite Element Methods for General Convection-Diffusion Equations

报告人：吴朔男 研究员（北京大学）

地点：致远楼101室

时间：2025年11月7日 16:00-17:00

摘要：This talk presents upwind-type stabilized finite element methods for convection-diffusion equations, focusing on recent extensions to vector-valued problems in H(curl)spaces. While exponential fitting provides an alternative stabilization strategy by incorporating boundary-layer characteristics, the discussion emphasizes upwind methods due to their adaptability in convection-dominated regimes. Two discontinuous Galerkin (DG) approaches—a primal DG and a hybridizable DG (HDG)—leverage weighted residual formulations and parameterized numerical traces to ensure stability and accuracy in magnetic advection-diffusion problems. Furthermore, other classical scalar techniques are generalized to H(curl)settings: a streamline upwind/Petrov-Galerkin (SUPG) method incorporates residual-based stabilization and a discrete advection operator, and a local projection stabilization (LPS) scheme enriches approximation spaces with H(curl)-conforming bubbles to satisfy local inf-sup conditions. These advances illustrate concrete approaches for designing and analyzing upwind-type discretizations for H(curl)convection-diffusion problems, demonstrating how classical scalar methodologies are adapted to the distinctive mathematical structure of vector field spaces.

报告人简介：吴朔男，北京大学长聘副教授/研究员，他分别于2009年和2014年在北京大学威廉希尔足球网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年加入北京大学威廉希尔足球网信息与计算科学系，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。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)。

欢迎各位参加！