An unconditionally gradient stable adaptive mesh refinement for the Cahn-Hilliard equation

Junseok Kim, Hyeong Ohk Bae

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We consider a numerical method, the so-called an unconditionally gradient stable adaptive mesh refinement scheme, for solving the Cahn-Hilliard equation representing a model of phase separation in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. An unconditionally gradient stable time discretization is used to remove the high-order time-step constraints. An adaptive mesh refinement is used to highly resolve narrow interfacial layers.

Original languageEnglish
Pages (from-to)672-679
Number of pages8
JournalJournal of the Korean Physical Society
Volume53
Issue number2
Publication statusPublished - 2008 Aug 1

Fingerprint

Hessian matrices
gradients
binary mixtures
eigenvalues
energy

Keywords

  • Adaptive mesh refinement
  • Cahn-Hilliard equation
  • Nonlinear multigrid method
  • Unconditionally stable scheme

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

An unconditionally gradient stable adaptive mesh refinement for the Cahn-Hilliard equation. / Kim, Junseok; Bae, Hyeong Ohk.

In: Journal of the Korean Physical Society, Vol. 53, No. 2, 01.08.2008, p. 672-679.

Research output: Contribution to journalArticle

@article{39c6f4f183bb48c890c810b2c3f9792e,
title = "An unconditionally gradient stable adaptive mesh refinement for the Cahn-Hilliard equation",
abstract = "We consider a numerical method, the so-called an unconditionally gradient stable adaptive mesh refinement scheme, for solving the Cahn-Hilliard equation representing a model of phase separation in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. An unconditionally gradient stable time discretization is used to remove the high-order time-step constraints. An adaptive mesh refinement is used to highly resolve narrow interfacial layers.",
keywords = "Adaptive mesh refinement, Cahn-Hilliard equation, Nonlinear multigrid method, Unconditionally stable scheme",
author = "Junseok Kim and Bae, {Hyeong Ohk}",
year = "2008",
month = "8",
day = "1",
language = "English",
volume = "53",
pages = "672--679",
journal = "Journal of the Korean Physical Society",
issn = "0374-4884",
publisher = "Korean Physical Society",
number = "2",

}

TY - JOUR

T1 - An unconditionally gradient stable adaptive mesh refinement for the Cahn-Hilliard equation

AU - Kim, Junseok

AU - Bae, Hyeong Ohk

PY - 2008/8/1

Y1 - 2008/8/1

N2 - We consider a numerical method, the so-called an unconditionally gradient stable adaptive mesh refinement scheme, for solving the Cahn-Hilliard equation representing a model of phase separation in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. An unconditionally gradient stable time discretization is used to remove the high-order time-step constraints. An adaptive mesh refinement is used to highly resolve narrow interfacial layers.

AB - We consider a numerical method, the so-called an unconditionally gradient stable adaptive mesh refinement scheme, for solving the Cahn-Hilliard equation representing a model of phase separation in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. An unconditionally gradient stable time discretization is used to remove the high-order time-step constraints. An adaptive mesh refinement is used to highly resolve narrow interfacial layers.

KW - Adaptive mesh refinement

KW - Cahn-Hilliard equation

KW - Nonlinear multigrid method

KW - Unconditionally stable scheme

UR - http://www.scopus.com/inward/record.url?scp=50949110245&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50949110245&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:50949110245

VL - 53

SP - 672

EP - 679

JO - Journal of the Korean Physical Society

JF - Journal of the Korean Physical Society

SN - 0374-4884

IS - 2

ER -