题目：High order kernel-based structrue-preserving methods for conservative PDEs or dissipative PDEs on surfaces

汇报人：孙正杰

会议时间：2024年5月17日16:00-16:50

地点：综合楼644会议室

报告人简介：孙正杰，南京理工大学数学与统计学院副教授，硕士生导师，香江学者，江苏省双创博士。2013年保送直博进入复旦大学数学科学学院，2018年入选“香江学者”博士后计划，在香港浸会大学从事博士后研究工作。主要研究径向基函数插值、拟插值方法以及无网格偏微分方程数值解法等，目前主持国家级和省级项目各一项，在SIAM J. SCI. Comput.、J. Comput. Phys.、J. Sci.Comput等期刊上发表论文20余篇。 现为中国工业与应用数学学会几何设计与计算专委会委员，中国数学会会员，江苏省计算数学学会理事。

摘要：In this talk, we introduce high order kernel-based meshless structrue-preserving methods for solving conservative PDEs or dissipative PDEs on surfaces. By posing the PDE in the variational formulation and simulating the solution in the finite-dimensional approximation space spanned by (local) Lagrange functions generated with positive definite kernels, we obtain a semi-discrete Galerkin equation that inherits the energy conservation or dissipation property. The fully-discrete structure-preserving scheme is derived with appropriate time integrators. We provide the full convergence analysis of the proposed method. The numerical experiments also verify the theoretical analysis including the convergence order and structure-preserving properties.