首页|Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation

Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation

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In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation,The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial discretization.In addition,two stabilization terms in different forms are added for the sake of the numerical stability.We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined estimate.By regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete l∞ bound of the numerical solution,as a result of the rough error estimate.Subsequently,the refined error estimate is derived to obtain the optimal rate of convergence,following the established l∞ bound of the numerical solution.Moreover,the energy stability is also rigorously proved with respect to a modified energy.The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.

nonlocal Cahn-Hilliard equationsecond-order stabilized schemehigher-order consistency analysisrough and refined error estimate

Xiao Li、Zhonghua Qiao、Cheng Wang

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Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong,China

Department of Mathematics,The University of Massachusetts,North Dartmouth,MA 02747,USA

Chinese Academy of Sciences(CAS)Academy of Mathematics and Systems Science(AMSS)Hong Kong Polytechnic University(PolyU)Joint Laboratory of Applied MathematicsHong Kong Research Council General Research FundHong Kong Polytechnic UniversityHong Kong Polytechnic UniversityHong Kong Polytechnic UniversityHong Kong Research Council Research Fellow SchemeGeneral Research FundUS National Science Foundation

153008211-BD8N4-ZZMK1-ZVWWRFS2021-5S0315302919DMS-2012269

2024

10.1007/s11425-022-2036-8

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(1)
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