Stabilized Finite Element Methods for General Convection-Diffusion Problems
数学专题报告
报告题目(Title)：Stabilized Finite Element Methods for General Convection-Diffusion Problems
报告人(Speaker)：吴朔男（北京大学）
地点(Place)：后主楼1124
时间(Time)：2026年9月23日（周三）16:00-17:00
邀请人(Inviter)：蔡勇勇
报告摘要
Convection-diffusion equations are fundamental models for transport phenomena and basic building blocks of many complex systems. In convection-dominated regimes, standard finite element methods may exhibit spurious oscillations. Starting from the scalar convection-diffusion equation, we discuss the origin of this instability and several classical stabilization mechanisms. We then consider their extensions to vector-field problems, with particular attention to H(curl) and H(div) formulations, and present the corresponding stability and approximation properties. Finally, we briefly discuss recent applications of convection-stable discretizations to energy-compatible numerical methods for non-Newtonian flows.
