报告问题 (Title)：Third order accurate, linear numerical scheme for epitaxial thin film growth model with energy stability（外延薄膜生长模子的三阶线性能量稳固数值名堂）

报告人 (Speaker)： 王成 教授（University of Massachusetts Dartmouth）

报告时间 (Time)：2022年9月21日(周三) 8:30

报告所在 (Place)：腾讯聚会（ID：931-330-657）

约请人(Inviter)：段成华

主理部分：理学院数学系

报告摘要：

A few linear schemes for nonlinear PDE model of thin film growth model without slope selection are presented in the talk. In the first order linear scheme, the idea of convex-concave decomposition of the energy functional is applied, and the particular decomposition places the nonlinear term in the concave part of the energy, in contrast to a standard decomposition. As a result, the numerical scheme is fully linear at each time step and unconditionally solvable, and an unconditional energy stability is guaranteed by the convexity splitting nature of the numerical scheme. To improve the numerical accuracy, a linear second order scheme is presented and analyzed, so that the energy stability is assured, with a second order Douglas-Dopnt regularization. Finally, a third order accurate ETD-based scheme is proposed, in which all the nonlinear terms are updated by higher order Lagrange extrapolation formulas. Moreover, the energy stability analysis and convergence estimate are established at a theoretical Level, which is the first such result in the area. Some numerical simulation results are also presented in the talk.