报告题目 (Title)：A second-order accurate, original energy dissipative
numerical scheme for the Patlak-Keller-Segel system （满足原始能量耗散Patlak-Keller-Segel系统的二阶数值格式）
报告人 (Speaker)：王成 教授（University of Massachusetts Dartmouth）
报告时间 (Time)：2026年6月30日（周三）10:00-12:00
报告地点 (Place)：宝山校区GJ303
邀请人(Inviter)：段成华
主办部门：理学院数学系
报告摘要：
A second-order accurate numerical scheme is proposed and analyzed for the Patlak-Keller-Segel system with various mobilities for the description of chemotaxis. Formulated in a variational structure, the entropy part is novelly discretized by a modified Crank-Nicolson approach so that the solution to the proposed nonlinear scheme corresponds to a minimizer of a convex functional. A careful theoretical analysis reveals that the unique solvability and positivity-preserving property could be theoretically justified. More importantly, such a second order numerical scheme is able to preserve the dissipative property of the original energy functional, instead of a modified one. In fact, the proposed scheme is the first such work in the existing literature, that is second order accurate and could achieve both the numerical positivity and original energy dissipation. In addition, an optimal rate convergence estimate is provided for the proposed scheme, in which rough and refined error estimate techniques have to be included to accomplish such an analysis. Some numerical results are presented to demonstrate robust performance of the proposed scheme.
