应兰州大学数学与统计学院宋伦继教授邀请，中国科学技术大学徐岩教授将于2026年7月18日举办线上学术报告。欢迎广大师生参加。

题目：High-order structure-preserving mimetic difference methods

时间：2026年7月18日14:30—15:15

地址：秦岭堂A112

腾讯会议号：953-444-882 密码：2026

摘要：We introduce a unified analytical framework for high-order numerical schemes based on mimetic discretization, applicable to a broad class of partial differential equations. The core of the framework lies in systematically characterizing the relationship between high-order and second-order mimetic operators. In particular, we show that high-order mimetic operators can be factorized into compositions of second-order mimetic operators and additional operators with simple structures.

Within this setting, we design reduction operators that simultaneously control high-order local truncation errors while preserving the intrinsic geometric and physical structures of the underlying problems. A central feature of the framework is the construction of a mimetic de Rham complex that forms an exact sequence and commutes with the corresponding continuous de Rham complex. Building on this structure-preserving formulation, we establish high-order a priori error estimates for a variety of model problems. Furthermore, the proposed approach naturally enforces key physical constraints, including curl-free conditions in acoustic equations and divergence-free properties in Maxwell's equations. These results demonstrate the effectiveness of the framework in achieving both high-order accuracy and structure preservation. For each problem, we provide numerical experiments to verify both the designed accuracy and the preservation of these structures. These results demonstrate the effectiveness of the framework in achieving both high-order accuracy and structure preservation.

报告人简介

徐岩，中国科学技术大学数学科学学院教授、博导，教育部长江学者奖励计划特聘教授,国家自然科学基金优秀青年基金、教育部新世纪优秀人才计划、中国数学会计算数学分会第二届“青年创新奖”获得者。主要研究领域为高精度数值计算方法。担任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、计算物理等杂志的编委。

甘肃省计算数学基础学科研究中心

数学与统计学院

萃英学院

2026年7月17日