An unconditionally gradient stable numerical method for the Ohta--Kawasaki model
Bull. Korean Math. Soc. 2017 Vol. 54, No. 1, 145-158
Published online January 4, 2017
Printed January 31, 2017
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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