题目：A Second-order Structure-preserving Parametric FEM for Surface Evolution

主讲人：杨宗泽 教授

时间：2026年5月28日（星期四）10：00

地点：理学院308会议室

主办单位：国家天元数学西北中心

理学院

主讲人简介：

杨宗泽，西北工业大学准聘教授，国家级青年人才，主要研究移动界面与非局部问题的数值方法及其应用。曾在北京计算科学研究中心、香港理工大学工作。获陕西高等学校科学技术研究优秀成果特等奖（R3），相关成果发表在Mathematics of Computation、SIAM Journal on Numerical Analysis、SIAM Journal on Scientific Computing、Journal of Computational Physics 等期刊。

摘要：

We propose a second-order-in-time, structure-preserving, and mesh-robust parametric finite element method for surface diffusion and volume-preserving mean curvature flow. The original evolution equations are first reformulated into new systems in which the tangential motion is governed by a harmonic map heat flow. This heat flow maps a fixed reference surface onto the evolving surface and induces tangential motion that reduces the associated harmonic energy. Consequently, in the discrete setting, the mesh quality can be maintained at a level comparable to that of the reference surface unless singularities occur. The volume-preserving property is theoretically guaranteed through a careful design of the scheme, while energy dissipation is enforced via a Lagrange multiplier. Several numerical experiments are presented to demonstrate the second-order temporal convergence and the effectiveness of the proposed method in maintaining mesh quality.