An r-adaptive finite element method for the solution of the two-dimensional phase-field equations

J. A. Mackenzie; M. L. Robertson; Mark George Beckett

An r-adaptive finite element method for the solution of the two-dimensional phase-field equations

J. A. Mackenzie, M. L. Robertson, Mark George Beckett

School of Physics and Astronomy

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

Abstract

An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Calerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.

Original language	English
Pages (from-to)	805-826
Number of pages	22
Journal	Communications in computational physics
Volume	1
Issue number	5
Publication status	Published - Oct 2006

Keywords

phase change
phase-field
equidistribution
moving meshes
adaptive method
MOVING MESH METHOD
NUMERICAL-SOLUTION
CRYSTAL-GROWTH
COMPUTATION
MODELS
SOLIDIFICATION
GENERATION
REFINEMENT
STEFAN
PDES

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title = "An r-adaptive finite element method for the solution of the two-dimensional phase-field equations",

abstract = "An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Calerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.",

keywords = "phase change, phase-field, equidistribution, moving meshes, adaptive method, MOVING MESH METHOD, NUMERICAL-SOLUTION, CRYSTAL-GROWTH, COMPUTATION, MODELS, SOLIDIFICATION, GENERATION, REFINEMENT, STEFAN, PDES",

author = "Mackenzie, {J. A.} and Robertson, {M. L.} and Beckett, {Mark George}",

year = "2006",

month = oct,

language = "English",

volume = "1",

pages = "805--826",

journal = "Communications in computational physics",

issn = "1815-2406",

publisher = "Global Science Press",

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TY - JOUR

T1 - An r-adaptive finite element method for the solution of the two-dimensional phase-field equations

AU - Mackenzie, J. A.

AU - Robertson, M. L.

AU - Beckett, Mark George

PY - 2006/10

Y1 - 2006/10

N2 - An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Calerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.

AB - An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Calerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.

KW - phase change

KW - phase-field

KW - equidistribution

KW - moving meshes

KW - adaptive method

KW - MOVING MESH METHOD

KW - NUMERICAL-SOLUTION

KW - CRYSTAL-GROWTH

KW - COMPUTATION

KW - MODELS

KW - SOLIDIFICATION

KW - GENERATION

KW - REFINEMENT

KW - STEFAN

KW - PDES

M3 - Article

VL - 1

SP - 805

EP - 826

JO - Communications in computational physics

JF - Communications in computational physics

SN - 1815-2406

IS - 5

ER -

An r-adaptive finite element method for the solution of the two-dimensional phase-field equations

Abstract

Keywords

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