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AN UNCONDITIONALLY GRADIENT STABLE NUMERICAL METHOD FOR THE OHTA-KAWASAKI MODEL

Authors
Kim, JunseokShin, Jaemin
Issue Date
1월-2017
Publisher
KOREAN MATHEMATICAL SOC
Keywords
block-copolymer; Ohta Kawasaki model; solvability; unconditionally gradient stability
Citation
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.54, no.1, pp.145 - 158
Indexed
SCIE
SCOPUS
KCI
Journal Title
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
Volume
54
Number
1
Start Page
145
End Page
158
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/84971
DOI
10.4134/BKMS.b150980
ISSN
1015-8634
Abstract
We present a finite difference method for solving the Ohta Kawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the Ohta Kawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.
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