报告一：Unconditional Superconvergence Analysis of a Linearized Mass and Energy Conservation Finite Element Method (FEM) for CNLS Equations

报告时间：9月21号14:30-15:30

报告地点：科教楼B座1710

报告人：石东洋 教授

工作单位：郑州大学

举办单位：3522vip浦京集团

报告人简介：石东洋，西安交通大学理学博士、东京工业大学博士后、河南省首批特聘教授（2003年）、郑州大学首批二级教授（2010年）、博士生导师（2000年）、烟台大学黄海学者特聘教授、河南省省级重点学科——计算数学学科带头人、学科特聘教授、河南省学术与技术带头人、河南省优秀专家、河南省高层次人才，河南省创新人才培养工程专家、河南省数学首席科普专家、河南省优秀教师、河南省首批优秀研究生指导教师（2022）、中国科协和教育部＂中学生英才计划＂十周年（2013一2022）优秀导师。国家自然科学基金项目（青年、面上、重点、杰青）通讯评审专家。主持国家自然科学基金7项（其中面上项目6项），省部级项目8项（其中人事部留学回国择优资助项目、教育部高等学校博士生点基金、河南省创新人才培养工程基金各1项）。发表SCI学术论文240余篇，培养硕士、博士130余人，主编《数值计算方法》，参编国家《数学大辞典》。获“中国百篇最具影响国内学术论文”2次。获省优秀科技成果及论文奖20项。2021年获河南自然科学奖二等奖。2022年入选全球顶尖前10万科学家全球学者库。

报告简介：This talk considers the unconditional superconvergence analysis of a linearized Crank-Nicolson fully-discrete scheme with FEM for CNLS equations .We show that this scheme has the mass and energy conservation properties and can lead to the superclose and superconvergence results through time-space splitting technique and interpolation post-processing approach. Some numerical tests are carried out to confirm the theoretical analysis

报告二：Efficient high-order semi-implicit spectral deferred correction time discretization for phase field models

报告时间：9月21号15:30-16:30

报告地点：科教楼B座1710

报告人：徐岩 教授

工作单位：中国科学技术大学

举办单位：3522vip浦京集团

报告人简介：徐岩，中国科学技术大学数学科学学院教授。2005年于中国科学技术大学数学系获计算数学博士学位。2005-2007年在荷兰Twente大学从事博士后研究工作。2009年获得德国洪堡基金会的支持在德国Freiburg大学访问工作一年。主要研究领域为高精度数值计算方法。2008年度获全国优秀博士学位论文奖，2017年获国家自然科学基金委“优秀青年基金”, 2017年获中国数学会计算数学分会第二届“青年创新奖”。徐岩教授入选了教育部新世纪优秀人才计划，主持国家自然科学基金面上项目、德国洪堡基金会研究组合作计划(Research Group Linkage Programme)、霍英东青年教师基础研究课题等科研项目。徐岩教授担任中国数学会计算数学分会理事，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。

报告简介：In this talk, we will present high order spectral deferred correction time discretization methods with energy stable linear schemes to simulate a series of phase field problems. The scheme also takes advantage of avoiding nonlinear iteration and the restriction of time step to guarantee the nonlinear system uniquely solvable. Moreover, the scheme leads to linear algebraic system to solve at each iteration, and we employ the multigrid solver to solve it efficiently. Numerical results are given to illustrate that the combination of local discontinuous Galerkin (LDG) spatial discretization and the high order temporal scheme is a practical, accurate and efficient simulation tool when solving phase field problems. Namely, we can obtain high order accuracy in both time and space by solving some simple linear algebraic equations. Numerical experiments are presented to demonstrate the accuracy, efficiency and robustness of the proposed semi-implicit time discretization methods for solving complex nonlinear PDEs.

报告三：Discontinuous Galerkin methods for the steady-state solutions of Euler equations

报告时间：9月21号16:30-17:30

报告地点：科教楼B座1710

报告人：夏银华 副教授

工作单位：中国科学技术大学

举办单位：3522vip浦京集团

报告人简介：夏银华，中国科学技术大学数学科学学院，副教授，博士生导师。中国科学技术大学数学系获得博士学位，曾先后到美国布朗大学、香港大学、德国维堡大学等从事博士后研究和访问工作。主要从事高精度数值方法和大规模科学计算的研究，应用于计算流体、天体物理、相场问题、交通流等方面的数值模拟。相关工作发表在包括Mathematics of Computation, Journal of Computational Physics, Journal of Scientific Computing,SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing等杂志。主持国家自然科学基金、教育部等多项科学基金项目的研究。担任美国数学会MathReview、德国数学文摘zbMATH评论员。

报告简介：In the realm of steady-state solutions of Euler equations, the pursuit of residue convergence to machine precision has been a persistent challenge for high-order shock-capturing schemes, especially in the presence of intense shock waves. To address this challenge, we have introduced a hybrid limiter within the framework of discontinuous Galerkin (DG) methods. This limiter integrates the jump indicator and limiter components seamlessly, yielding a more cohesive and efficient approach. For steady-state problems, we have utilized the hybridization of the DG solution with the cell average, eliminating the necessity for characteristic decomposition and intercell communication, thereby significantly reducing computational costs and enhancing parallel efficiency. Additionally, we have developed a novel jump filter, which operates locally based on jump information at cell interfaces, targeting high-order polynomial modes within each cell. This filter not only retains the localized nature but also preserves the key attributes of the DG method, including conservation, L2 stability, and high-order accuracy. We have also explored its compatibility with other damping techniques and demonstrated its seamless integration into a hybrid limiter. Numerical experiments are presented to illustrate the robust performance of these schemes for steady Euler equations on both structured and unstructured meshes.