Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.05.014 ◽

2021 ◽

Vol 96 ◽

pp. 67-76

Author(s):

Huanrong Li ◽

Dongmei Wang ◽

Zhengyuan Song ◽

Fuchen Zhang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Analysis ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Reduced Order ◽

Energy Stable ◽

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Decoupled, Linear, and Energy Stable Finite Element Method for the Cahn--Hilliard--Navier--Stokes--Darcy Phase Field Model

SIAM Journal on Scientific Computing ◽

10.1137/16m1100885 ◽

2018 ◽

Vol 40 (1) ◽

pp. B110-B137 ◽

Author(s):

Yali Gao ◽

Xiaoming He ◽

Liquan Mei ◽

Xiaofeng Yang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Navier Stokes ◽

Energy Stable ◽

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A phase-field model for simulation of the laser cladding process using a discontinuous viscosity variable and its approximation by finite element method

International Congress on Applications of Lasers & Electro-Optics ◽

10.2351/1.5060380 ◽

2004 ◽

Author(s):

Aaron Naber ◽

Richard Martukanitz

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Laser Cladding ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Laser Cladding Process ◽

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Full Eulerian finite element method of a phase field model for fluid–structure interaction problem

Computers & Fluids ◽

10.1016/j.compfluid.2013.11.010 ◽

2014 ◽

Vol 90 ◽

pp. 1-8 ◽

Author(s):

Pengtao Sun ◽

Jinchao Xu ◽

Lixiang Zhang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Phase Field ◽

Field Model ◽

Fluid Structure Interaction ◽

Phase Field Model ◽

Fluid Structure ◽

Structure Interaction ◽

Interaction Problem ◽

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Analysis of Transformation Plasticity in Steel Using a Finite Element Method Coupled with a Phase Field Model

PLoS ONE ◽

10.1371/journal.pone.0035987 ◽

2012 ◽

Vol 7 (4) ◽

pp. e35987 ◽

Author(s):

Yi-Gil Cho ◽

Jin-You Kim ◽

Hoon-Hwe Cho ◽

Pil-Ryung Cha ◽

Dong-Woo Suh ◽

...

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Transformation Plasticity ◽

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A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets

Communications in Computational Physics ◽

10.4208/cicp.oa-2017-0166 ◽

2019 ◽

Vol 25 (1) ◽

Author(s):

Amanda E. Diegel ◽

Shawn W. Walker

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

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Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and its Numerical Simulations with Mixed Finite Element Method

Communications in Computational Physics ◽

10.4208/cicp.2009.v6.p1095 ◽

2009 ◽

Vol 6 (5) ◽

pp. 1095-1117 ◽

Author(s):

Pengtao Sun ◽

Chun Liu ◽

Jinchao Xu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Simulations ◽

Phase Field ◽

Field Model ◽

Mixed Finite Element ◽

Phase Field Model ◽

Mixed Finite Element Method ◽

Marangoni Effects ◽

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Convergence of the finite element method applied to an anisotropic phase-field model

Annales mathématiques Blaise Pascal ◽

10.5802/ambp.186 ◽

2004 ◽

Vol 11 (1) ◽

pp. 67-94 ◽

Author(s):

Erik Burman ◽

Daniel Kessler ◽

Jacques Rappaz

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

The Finite Element Method ◽

Anisotropic Phase ◽

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Analysis of a fully discrete finite element method for the phase field model and approximation of its sharp interface limits

Mathematics of Computation ◽

10.1090/s0025-5718-03-01588-6 ◽

2003 ◽

Vol 73 (246) ◽

pp. 541-568 ◽

Author(s):

Xiaobing Feng ◽

Andreas Prohl

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Sharp Interface ◽

Fully Discrete ◽

Discrete Finite Element ◽

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Two-phase flow analysis based on a phase-field model using orthogonal basis bubble function finite element method

International Journal of Computational Fluid Dynamics ◽

10.1080/10618560802238226 ◽

2008 ◽

Vol 22 (8) ◽

pp. 555-568 ◽

Author(s):

Junichi Matsumoto ◽

Naoki Takada

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Phase Field ◽

Field Model ◽

Flow Analysis ◽

Phase Field Model ◽

Orthogonal Basis ◽

Two Phase ◽

Bubble Function

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3D adaptive finite element method for a phase field model for the moving contact line problems

Inverse Problems & Imaging ◽

10.3934/ipi.2013.7.947 ◽

2013 ◽

Vol 7 (3) ◽

pp. 947-959 ◽

Author(s):

Yi Shi ◽

◽

Kai Bao ◽

Xiao-Ping Wang ◽

◽

...

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Contact Line ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Adaptive Finite Element Method ◽

Adaptive Finite Element ◽

Moving Contact Line ◽

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