学术报告

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

报告人：王成 （美国麻省大学达特茅斯分校副教授）

报告时间：6月22 日上午9:00—9:45      

报告地点：数统院307

                                           红世一足666814

                                             2019.06.20

‍

报告摘要：A few fully discrete numerical schemes for the Cahn-Hilliard-Hele-Shaw andCahnn-Hilliard-stokes equations,a modified phase field model coupled with withthe the Darcy or Stokes flow law, are analyzed in details. The uniquesolvability comes from the variational calculation, while and unconditionalenergy stability comes from the energy estimate. In turn, a uniform in time H^1bound for the numerical solution becomes available.

    Moreover, with the help ofdiscrete Gagliardo-Nirenberg type inequality, derived in terms of discreteFourier analysis, we are able to obtain the L^2 (0,T; H^3) stability of thenumerical solution. Subsequently, we perform a discrete L^\infty (0,T; H^1) andL^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 totreat the nonlinear convection term in a positive way, since one essentialnonlinear inner product turns out to be non-negative. Some numerical simulationresults 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 obtainedhid 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 thesupervision of Roger Temam and Shouhong Wang, and he worked as an assistantprofessor at University of Tennessee at Knoxville from 2003 to 2008. Dr. Wang’sresearch interests include development of stable, accurate numerical algorithmsfor partial differential equations and numerical analysis. He has publishedmore than 70 papers with more than 1800 citations. He also serves in theEditorial Board of “Numerical Mathematics: Theory, Methods andApplications”.