报告人：周兆杰 教授 山东师范大学
报告题目：Adaptive finite element approximation of semilinear fractional optimal control problem
摘 要：This talk investigates adaptive finite element approximation of fractional semilinear optimal control problems involving the integral fractional Laplacian. We consider two finite element discrete schemes: the state and adjoint state are both discretized by piecewise linear functions, while the control variable is approximated by variational discretization and piecewise constant functions, respectively. To effectively resolve the typically singular or highly localized behavior of the solutions near boundaries or specific points, we construct reliable residual-based a posteriori error estimators based on the estimate of the Scott-Zhang operator in fractional Sobolev space and the property of the first derivative of the reduced cost functional. Numerical experiments confirm the theoretical findings.
报告人简介：周兆杰教授，山东师范大学数学与统计学院副院长、博士生导师。主要研究方向为偏微分方程约束最优控制问题的数值算法，发表学术论文70余篇，主持国家自然科学基金项目、山东省自然科学基金项目多项，获山东省自然科学二等奖1项；兼任中国工业与应用数学学会理事、中国数学会计算数学分会理事、山东省数学会理事。
报告时间：2025年12月24日，8:30--11:30
报告地点：腾讯会议（会议号：278-567-712）
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内蒙古大学数学科学学院
2025年12月22日
蒙ICP16002391号-1