报告人: 陈艳萍教授，南京邮电大学

时间: 2024.07.08, 周一, 下午4:00-5:00

地点: 维格堂319

摘要:  Theoretical analysis of the three-step backward difference formula (BDF3) with variable step-sizes for parabolic equations is highly nontrivial so far. In this talk, we report the positive definiteness property of the variable-step BDF3 method by establishing a gradient decomposition under a new restriction $0.5\leq \rho_n\leq 1.7319$, where $\rho_n$ is the adjacent step-size ratio. The condition improves the upper bound of the step-size ratio in existing results, and is significant for the subsequent stability and convergence analysis. An original framework to analyze the variable-step BDF3 schemes for parabolic equations is provided under the new condition. In addition, the Cahn-Hilliard equation is taken as a nonlinear prototype to elucidate the proposed framework, for which the energy stability and optimal third order convergence rate are both derived rigorously. Several numerical examples verify the accuracy and efficiency of the developed method.

陈艳萍，南京邮电大学博士生导师、国务院政府特殊津贴专家、教育部新世纪人才。中国工业与应用数学学会油水资源数值方法专业委员会副主任、国际数学建模挑战赛专家委员会和学术及顾问委员、国际 SCI 学术期刊《AAMM》编委。主持获得教育部自然科学二等奖和广东省科学技术二等奖、参与获得国家教学成果二等奖和教育部自然科学一等奖等等。2014-2023 年连续 10 年入选 Elsevier 中国高被引学者榜单，入选 2023 全球顶尖前 10 万科学家排名和数学类全球前 2%顶尖科学家榜单。主持国家自然科学基金重点项目 1 项和面上项目 8 项。

邀请人：岳兴业