报告题目：Maximum-principle-preserving local discontinuous Galerkin methods for KdV-type equations

摘      要：In this paper, we construct the maximum-principle-preserving (MPP) local discontinuous Galerkin (LDG) method for the generalized third-order Korteweg-de Vries (KdV) equation. The third-order strong stability preserving (SSP) Runge-Kutta method is employed to time discretization. Motivated by Du and Yang (2019) , we consider the MPP technique of the KdV equation on nonuniform meshes (i.e., rewriting the fully discrete LDG scheme through constructing the mapping between the nonuniform meshes and [−1, 1]) so that we obtain the sufficient conditions that make LDG methods satisfy the maximum principle to limit time step ∆t. Furthermore, we use the idea in Zhang and Shu (2010) to construct the slope limiter as a post-processing implement of LDG methods. Then, we extend the scheme to the two-dimensional Zakharov-Kuznetsov (ZK) equation. The accuracy and the performance of bound-preserving, under the conditions of zero dispersion limit and positive dispersion coefficient, will be demonstrated in numerical experiments.

报告时间：2023年4月14日星期五下午2:00-3:00

报告地点：2号教学楼403

报告人简介：毕卉，哈尔滨理工大学应用数学系教授，博士生导师，应用数学系主任。2011年于哈尔滨工业大学获得博士学位，研究方向为偏微分方程数值解、微分形式算子理论。在Comp. Math. Appl., J. Appl. Anal. Comp.等杂志发表SCI论文10余篇。主持完成国家自然科学基金1项，教育厅基金2项，在研省基金和高校专项基金各1项，担任黑龙江省数学会常务理事，SCI杂志JIA副主编。