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报告题目：Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model
报 告 人：王成教授 马萨诸塞大学
报告摘要：Positivity preserving, energy stable numerical schemes are proposed and analyzed for the droplet liquid film model, with a singular Leonard-Jones energy potential involved. Both the first and second order accurate temporal algorithms are considered. In the first order scheme, the convex potential and the surface diffusion terms are implicitly, while the concave potential term is updated explicitly. Furthermore, we provide a theoretical justification that this numerical algorithm has a unique solution, such that the positivity is always preserved for the phase variable at a point-wise level. Moreover, an unconditional energy stability of the numerical scheme is derived, without any restriction for the time step size. In the second order numerical scheme, the BDF temporal stencil is applied, and an alternate convex-concave decomposition is derived, so that the concave part corresponds to a quadratic energy. In turn, the combined Leonard-Jones potential term is treated implicitly, and the concave part the is approximated by a second order Adams-Bashforth explicit extrapolation, and an artificial Douglas-Dupont regularization term is added to ensure the energy stability. The unique solvability and the positivity-preserving property for the second order scheme are similarly established. In addition, optimal rate convergence analysis is derived for both numerical schemes. A few numerical simulation results are also presented.
报告人简介：王成教授是马萨诸塞大学达特茅斯分校数学系教授。2000年获美国天普大学博士学位，师从刘建国教授。在2008年加入马萨诸塞大学担任助理教授之前，他于2000年至2003年在印第安纳大学担任Zorn博士后，师从Roger Temam和Wang Shouhong； 2003年至2008年在田纳西大学诺克斯维尔分校担任助理教授。他的研究兴趣包括开发稳定、精确的偏微分方程数值算法和数值分析。发表论文130余篇，被引用7000余次。他还曾担任《Numerical Mathematics: Theory, Methods and Applications》编委。
报告时间：2025年12月25日 14:30-16:00
报告地点：文渊楼 B536
主办单位：数学与统计学院
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