A general class of linear unconditionally energy stable schemes for the gradient flows

主讲人：谈增强（武汉理工大学）

摘要：This talk introduces linear, unconditionally energy stable numerical schemes for gradient flows, which are built on the SAV technique and the general linear time discretizations (GLTD). We first consider algebraically stable GLTDs. Theoretical analysis verifies the unconditional energy stability of the semi-discrete time schemes, whose convergence order is determined by the generalized stage order of GLTDs and the number of temporal extrapolation points under diagonal stability, proper regularity conditions and accurate initial values. Second, a three-parameter SAV-GL scheme is developed. By adopting the undetermined coefficient method, algebraic identities and corresponding modified energy inequalities are derived to guarantee the unconditional modified energy stability of the semi-discrete schemes, and these stability inequality are non-unique. Numerical experiments on the Allen-Cahn, Cahn-Hilliard, and phase field crystal models are implemented to validate the stability, accuracy and effectiveness of the proposed schemes. Additionally, the time step constraints for maintaining monotonic decay of original energy are estimated via stability regions of test equations, which are well consistent with the numerical results.

主讲人简介：谈增强，武汉理工大学数学科学研究中心讲师。2021年毕业于华中科技大学并获得理学博士学位，2019-2020在美国密歇根州立大学联合培养，2021-2023在北京大学数学科学学院从事博士后研究.主要研究方向是偏微分方程的高精度保结构数值算法和自适应移动网格等。目前在JCP、CiCP、ANM、CNSNS等SCI期刊发表论文十六篇，主持国家留学基金委项目一项，国家自然科学基金青年项目一项，主持湖北省博士后先锋人才跟踪项目等。

邀请人：张诚坚

时间：2026年8月29日8:30-10:30

地点： 科技楼南楼706室