發表時間:2021-01-12 閱讀次數:1310次
報告題目: Optimal rate convergence analysis and error estimate of a finite difference scheme for the Ericksen-Leslie ystem with the penalty function
報 告 人:Cheng Wang 教授
報告人所在單位:Department of Mathematics, the University of Massachusetts, North Dartmouth, USA.
報告日期:2021-01-12 星期二
報告時間:9:30-10:30
報告地點:Zoom會議號 64531581235,密碼:888888
  
報告摘要:

A first order accurate in time, finite difference scheme is proposed and analyzed for the Ericksen-Leslie system, which describes motions of nematic liquid crystals. For the penalty function to approximate the phase field constraint, a convex-concave decomposition for the corresponding energy functional is applied. In addition, appropriate semi-implicit treatments are adopted to the convection terms, for both the velocity vector and orientation vector, as well as the the coupled elastic stress terms. In turn, all the semi-implicit terms could be represented as a linear operator of a vector potential, and its combination with the convex splitting discretization for the penalty function leads to a unique solvability analysis for the proposed numerical scheme. Furthermore, a careful estimate reveals an unconditional energy stability of the numerical system, composed of the kinematic energy and internal elastic energies. More importantly, an optimal rate convergence analysis and error estimate for the numerical scheme, which will be the first such result in the area.

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本年度學院報告總序號:4

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