NUMERICAL ENERGY DISSIPATION FOR TIME-FRACTIONAL PHASE-FIELD EQUATIONS  

作　　者：Chaoyu Quan Tao Tang Jiang Yang 

机构地区：[1]School of Science and Engineering,The Chinese University of Hong Kong,Shenzhen 518172,China [2]Division of Science and Technology,BNU-HKBU United International College,Zhuhai 519087,China [3]Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNU-HKBU United International College,Zhuhai 519087,China [4]Department of Mathematics,SUSTech International Center for Mathematics&National Center for Applied Mathematics Shenzhen(NCAMS),Southern University of Science and Technology,Shenzhen 518055,China

出　　处：《Journal of Computational Mathematics》2025年第3期515-539,共25页计算数学(英文)

基　　金：supported by the NSFC/Hong Kong RGC Joint Research Scheme(Grant No.NSFC/RGC 11961160718);supported by the National Natural Science Foundation of China(NSFC)(Grant No.12271240);by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design,China(Grant No.2019B030301001);by the Shenzhen Natural Science Fund(Grant No.RCJC20210609103819018);supported by the NSFC(Grant No.12271241);by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023B1515020030);by the Shenzhen Science and Technology Program(Grant Nos.RCYX2021060,9104358076).

摘　　要：The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle.Although the theory of energy dissipation for classical phase field models is well established,the corresponding theory for time-fractional phase-field models is still incomplete.In this article,we study certain nonlocal-in-time energies using the first-order stabilized semi-implicit L1 scheme.In particular,we will establish a discrete fractional energy law and a discrete weighted energy law.The extension for a(2-α)-order L1 scalar auxiliary variable scheme will be investigated.Moreover,we demonstrate that the energy bound is preserved for the L1 schemes with nonuniform time steps.Several numerical experiments are carried to verify our theoretical analysis.

关 键 词：Time-fractional phased-field equation Allen-Cahn equations Cahn-Hilliard equations Caputo fractional derivative Energy dissipation 

分 类 号：O241.82[理学—计算数学]