Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(1): 145-158

Online first article January 4, 2017      Printed January 31, 2017

https://doi.org/10.4134/BKMS.b150980

Copyright © The Korean Mathematical Society.

An unconditionally gradient stable numerical method for the Ohta--Kawasaki model

Junseok Kim and Jaemin Shin

Korea University, Ewha W. University

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.

Keywords: block-copolymer, Ohta--Kawasaki model, solvability, unconditionally gradient stability

MSC numbers: Primary 65M06, 65M55

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