A multigrid method for the Cahn-Hilliard equation with obstacle potential

Lubomir Banas; Robert Nürnberg

doi:10.1016/j.amc.2009.03.036

A multigrid method for the Cahn-Hilliard equation with obstacle potential

Lubomir Banas, Robert Nürnberg

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

We present a multigrid finite element method for the deep quench obstacle Cahn-Hilliard equation. The non-smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging. The method exhibits mesh-independent convergence properties in practice for arbitrary time step sizes. In addition, numerical evidence shows that this behaviour extends to small values of the interfacial parameter ?. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation. © 2009 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	290-303
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	213
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2009.03.036
Publication status	Published - 15 Jul 2009

Keywords

Cahn-Hilliard equation
Finite elements
Multigrid method
Obstacle free energy

Access to Document

10.1016/j.amc.2009.03.036

Cite this

@article{df0dd0df02094fb18d86781fab0fa426,

title = "A multigrid method for the Cahn-Hilliard equation with obstacle potential",

abstract = "We present a multigrid finite element method for the deep quench obstacle Cahn-Hilliard equation. The non-smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging. The method exhibits mesh-independent convergence properties in practice for arbitrary time step sizes. In addition, numerical evidence shows that this behaviour extends to small values of the interfacial parameter ?. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation. {\textcopyright} 2009 Elsevier Inc. All rights reserved.",

keywords = "Cahn-Hilliard equation, Finite elements, Multigrid method, Obstacle free energy",

author = "Lubomir Banas and Robert N{\"u}rnberg",

year = "2009",

month = jul,

day = "15",

doi = "10.1016/j.amc.2009.03.036",

language = "English",

volume = "213",

pages = "290--303",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - A multigrid method for the Cahn-Hilliard equation with obstacle potential

AU - Banas, Lubomir

AU - Nürnberg, Robert

PY - 2009/7/15

Y1 - 2009/7/15

N2 - We present a multigrid finite element method for the deep quench obstacle Cahn-Hilliard equation. The non-smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging. The method exhibits mesh-independent convergence properties in practice for arbitrary time step sizes. In addition, numerical evidence shows that this behaviour extends to small values of the interfacial parameter ?. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation. © 2009 Elsevier Inc. All rights reserved.

AB - We present a multigrid finite element method for the deep quench obstacle Cahn-Hilliard equation. The non-smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging. The method exhibits mesh-independent convergence properties in practice for arbitrary time step sizes. In addition, numerical evidence shows that this behaviour extends to small values of the interfacial parameter ?. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation. © 2009 Elsevier Inc. All rights reserved.

KW - Cahn-Hilliard equation

KW - Finite elements

KW - Multigrid method

KW - Obstacle free energy

UR - http://www.scopus.com/inward/record.url?scp=67349109199&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2009.03.036

DO - 10.1016/j.amc.2009.03.036

M3 - Article

VL - 213

SP - 290

EP - 303

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 2

ER -

A multigrid method for the Cahn-Hilliard equation with obstacle potential

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this