演讲人Speaker：

李猛 副教授

题目Title:  

Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: a unified framework

时间Date& Time：  

2021 年 6 月 25日      09：00--10：00

地点Venue：  

腾讯会议 ID：962 655 270

内容摘要Abstract：

We present, in a unified framework, conforming and nonconforming virtual element methods for nonlinear Schrödinger equation. The constructed schemes conserve not only the mass but also the energy in the discrete senses. Then, by using the Brouwder fixed point theorem, the Gagliardo-Nirenberg inequality and the classical Ritz projection, we prove the boundedness, unique solvability and optimal convergence of the conforming virtual element scheme. To obtain the boundedness, unique solvability and optimal convergence of the nonconforming virtual element scheme, we utilize a new defined Ritz projection and a new type of Gagliardo-Nirenberg inequality. The optimal rates of convergence in the discrete L^2-norm are derived without any restrictions on the grid ratio for both types of virtual element methods. Finally, numerical examples on a set of polygonal meshes are given to support the theoretical analysis. As a contrast, we also supply another classical proof method of the optimal convergence which has to limit the time-space grid ratio.

个人简介About the speaker:

李猛，博士，郑州大学直聘副教授，硕士研究生导师。2017年6月毕业于华中科技大学数学与统计学院，获得博士学位，于2017年7月入职郑州大学。导师为陈绍春教授（硕士）、黄乘明教授（博士），以及石东洋教授（博士后）。主要研究方向为偏微分方程数值解，研究方法主要包括：虚拟元方法、有限元方法、谱方法以及配置方法，目前主要研究非线性（局部及非局部）模型的保结构算法、快速算法以及机器学习等。在IMA Journal of Numerical Analysis, Computer Methods in Applied Mechanics and Engineering, Journal of Computational Physics, Journal of Scientific Computing, BIT Numerical Mathematics等SCI期刊上发表学术论文三十余篇，其中多篇入选ESI高被引论文，目前主持国家自然科学基金青年项目和中国博士后面上项目，获得2021年度河南省优秀科技论文一等奖。