演讲人Speaker：Cheng Wang 教授

题目Title:  Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model

时间Date：  2021年11月5日Time：9：00--10：00

地点Venue： Zoom会议室

https://umassd.zoom.us/j/6339263022（密码：123456）

内容摘要Abstract：

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. 

个人简介(About the speaker):

Dr. Cheng Wang is a professor in Department of  Mathematics at the University of Massachusetts Dartmouth  (UMassD). He obtained hid Ph.D degree from Temple University in 2000, under the supervision of  Prof. Jian-Guo Liu. Prior to joining UMassD in 2008 as an assistant professor, he was a Zorn postdoc at Indiana University from 2000 to 2003, under the supervision of Roger Temam and Shouhong Wang, and he worked as an assistant professor at University of Tennessee at Knoxville from 2003 to 2008. Dr. Wang’s research interests include development of stable, accurate numerical algorithms for partial differential equations and numerical analysis. He has published more than 80 papers with more than 5000 citations. He also serves in the Editorial Board of “Numerical Mathematics: Theory, Methods and Applications”.