Compatible L2 norm convergence of the variable-step L1 energy stable scheme for the TFMBE model

主讲人：杨银

摘要：The convergence of the variable-step L1 schemes is studied for the time-fractional molecular beam epitaxy (TFMBE) model with or without slope selection. By taking advantage of the convex splitting of nonlinear bulk, novel asymptotically compatible L2 norm error estimates of the variable-step L1 schemes are established under a convergence-solvability-stability(CSS)-consistent time-step constraint. The CSS-consistent condition means that the maximum step-size limit required for convergence is of the same order as that for solvability and stability (in certain norms) as the small interface parameter. To the best of our knowledge, it is the first time to establish such an error estimate for nonlinear subdiffusion problems. The asymptotically compatible convergence means that the error estimate is compatible with that of the backward Euler scheme for the classical MBE model as the fractional order →. Just as the backward Euler scheme can maintain the physical properties of the MBE equation, the variable-step L1 scheme can also preserve the corresponding properties of the TFMBE model, including the volume conservation, variational energy dissipation law and L2 norm boundedness. Numerical experiments are presented to support our theoretical results.

主讲人简介：杨银，湘潭大学教授，博士生导师。现任湘潭大学数学与计算科学学院院长、湖南国家应用数学中心常务副主任。主持国家重大研究计划项目课题1项、国家自然科学基金中俄国际合作项目1项、国家自然科学基金项目4项，发表学术论文50余篇；获宝钢优秀教师奖、湖南省科技创新领军人才、湖南省杰出青年基金、湖南省"芙蓉学者奖励计划"青年学者等奖励荣誉。

邀请人：张诚坚

时间：2023年5月12日（星期五）20:30-22:30