报告人：刘文杰（哈尔滨工业大学）

报告时间：2026年4月24日（星期五）10:00-12:00

报告地点：科技楼南楼702室

报告摘要：The hp local discontinuous Galerkin (LDG) method proposed by Castillo et al. [Math. Comp., 71 (238): 455–478, 2002] has been shown to be an efficient approach for solving convection–diffusion equations. However, theoretical analysis indicates that, for solutions with limited spatial regularity, the method exhibits suboptimal convergence in p, suffering a loss of one order, comparing to numerical experiments. In this talk, we address this discrepancy between theory and computation. We develop new approximation results for Gauss–Radau projections within appropriately chosen function spaces that capture the intrinsic regularity of singular solutions. This framework arises naturally and allows for a unified treatment of various types of low-regularity solutions. Our analysis demonstrates that, under this refined perspective, the hp-LDG method achieves optimal convergence in p, fully consistent with numerical evidence.

报告人简介：刘文杰，哈尔滨工业大学数学学院副教授，博士生导师。2012年和2016年于哈尔滨工业大学数学学院获得硕士学位和博士学位，2016年11月至2017年11月在新加坡南洋理工大学从事博士后研究。主要研究方向为具奇异性问题的多项式逼近理论、具奇异性偏微分方程谱元法的误差估计等。发表学术论文30余篇，部分论文发表于 Mathematics of Computation、 Journal of Approximation Theory和 Journal of Computational Physics等。其研究工作获得国家自然科学基金面上项目、天元东北中心优秀青年学者奖励计划和黑龙江省优秀青年基金等项目的资助。

邀请人：王海永