报告题目：Optimal rate convergence analysis for phase field equation coupled with fluid flow

报 告 人：王成副教授（美国麻省大学达特茅斯分校）

报告时间：2019年6月22日 9:00-9:45

报告地点：数统院307学术报告厅

报告摘要：

A few fully discrete numerical schemes for the Cahn-Hilliard-Hele-Shaw and Cahnn-Hilliard-stokes equations, a modified phase field model coupled with with the the Darcy or Stokes flow law, are analyzed in details. The unique solvability comes from the variational calculation, while and unconditional energy stability comes from the energy estimate. In turn, a uniform in time H^1 bound for the numerical solution becomes available. Moreover, with the help of discrete Gagliardo-Nirenberg type inequality, derived in terms of discrete Fourier analysis, we are able to obtain the L^2 (0,T; H^3) stability of the numerical solution. Subsequently, we perform a discrete L^\infty (0,T; H^1) and L^2 (0,T; H^3) error estimate, instead of the L^\infty (0,T;L^2) and L^2 (0,T; H^2)$ one, which represents the typical analysis. Such an approach allows us to treat the nonlinear convection term in a positive way, since one essential nonlinear inner product turns out to be non-negative. Some numerical simulation results are also presented in the talk.

报告人简介：

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 70 papers with more.