题目：Refined implicit-explicit Runge-Kutta methods with robust time adaptability for the Cahn-Hilliard model

摘要：One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of stage solutions without the global Lipschitz continuity assumption of nonlinear bulk. With the help of discrete orthogonal convolution kernels, an updated time-space splitting technique is developed to establish the uniform boundedness of stage solutions for a refined class of IERK methods in which the associated differentiation matrices and the average dissipation rates are always independent of the time-space discretization meshes. This makes the refined IERK methods highly advantageous in self-adaptive time-stepping procedures as some larger adaptive step-sizes in actual simulations become possible. From the perspective of optimizing the average dissipation rate, we construct some parameterized refined IERK methods up to third-order accuracy, in which the involved diagonally implicit Runge-Kutta methods for the implicit part have an explicit first stage and allow a stage-order of two such that they are not necessarily algebraically stable. Then we are able to establish, for the first time, the original energy dissipation law and the unconditional $L^2$ norm convergence. Extensive numerical tests are presented to support our theory.

报告人：廖洪林教授，南京航空航天大学

时间：2026年5月16日16:00

地点：知新楼B座924

报告人简介：

廖洪林，应用数学博士、教授，2018年至今任教于南京航空航天大学数学学院。2010年获理学博士学位，2001-2017年任教于原解放军理工大学、陆军工程大学。学术研究方向为偏微分方程数值解，目前主要关注非线性相场以及多相流模型的高阶时间离散与时间自适应算法，在Math Comp，SIAM J Numer Anal, SIAM J Sci Comput，IMA J Numer Anal，J Comput Phys，Sci China Math等国内外专业期刊上发表学术研究论文五十余篇。相关研究工作得到了国内外同行的广泛关注与认可、引发了很多后续研究工作，在WOS上他引3100余次（总引3300余次）。近年来有16篇研究论文入选ESI高被引论文，2024-2025连续两年入选Elsevier全球前2%顶尖科学家年度榜单、2025年入选Clarivate全球高被引研究者榜单。

邀请人：芮洪兴