A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.10.029 ◽

2021 ◽

Vol 103 ◽

pp. 104-126

Author(s):

Shuaichao Pei ◽

Yanren Hou ◽

Qi Li

Keyword(s):

Error Estimates ◽

Phase Field ◽

Second Order ◽

Energy Stable ◽

Energy Stable Scheme ◽

Stable Scheme ◽

Phase Field Crystal

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A linearly second-order energy stable scheme for the phase field crystal model

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.01.017 ◽

2019 ◽

Vol 140 ◽

pp. 134-164 ◽

Author(s):

Shuaichao Pei ◽

Yanren Hou ◽

Bo You

Keyword(s):

Phase Field ◽

Second Order ◽

Order Energy ◽

Crystal Model ◽

Energy Stable ◽

Energy Stable Scheme ◽

Stable Scheme ◽

Phase Field Crystal

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A novel fully-decoupled, second-order time-accurate, unconditionally energy stable scheme for a flow-coupled volume-conserved phase-field elastic bending energy model

Journal of Computational Physics ◽

10.1016/j.jcp.2020.110015 ◽

2021 ◽

Vol 432 ◽

pp. 110015 ◽

Author(s):

Xiaofeng Yang

Keyword(s):

Phase Field ◽

Energy Model ◽

Second Order ◽

Bending Energy ◽

Elastic Bending ◽

Energy Stable ◽

Energy Stable Scheme ◽

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Efficient, Second-Order in Time, and Energy Stable Scheme for a New Hydrodynamically Coupled Three Components Volume-Conserved Allen-Cahn Phase-Field Model

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202521500184 ◽

2021 ◽

Author(s):

Xiaofeng Yang

Keyword(s):

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Second Order ◽

Second Order In Time ◽

Energy Stable ◽

Time And Energy ◽

Energy Stable Scheme ◽

Stable Scheme ◽

Three Components

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Error estimates for second-order SAV finite element method to phase field crystal model

Electronic Research Archive ◽

10.3934/era.2020089 ◽

2021 ◽

Vol 29 (1) ◽

pp. 1735-1752

Author(s):

Liupeng Wang ◽

◽

Yunqing Huang ◽

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Error Estimates ◽

Phase Field ◽

Second Order ◽

Crystal Model ◽

Element Method ◽

Phase Field Crystal

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Fully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities

Applied Mathematical Modelling ◽

10.1016/j.apm.2020.02.022 ◽

2020 ◽

Vol 83 ◽

pp. 614-639 ◽

Author(s):

Guangpu Zhu ◽

Huangxin Chen ◽

Aifen Li ◽

Shuyu Sun ◽

Jun Yao

Keyword(s):

Contact Line ◽

Phase Field ◽

Discrete Energy ◽

Fully Discrete ◽

Moving Contact Line ◽

Moving Contact ◽

Energy Stable ◽

Energy Stable Scheme ◽

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Linear second order energy stable schemes for phase field crystal growth models with nonlocal constraints

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.07.030 ◽

2020 ◽

Vol 79 (3) ◽

pp. 764-788 ◽

Author(s):

Xiaobo Jing ◽

Qi Wang

Keyword(s):

Crystal Growth ◽

Phase Field ◽

Growth Models ◽

Second Order ◽

Order Energy ◽

Energy Stable Schemes ◽

Energy Stable ◽

Nonlocal Constraints ◽

Phase Field Crystal

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First- and second-order energy stable methods for the modified phase field crystal equation

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2017.03.033 ◽

2017 ◽

Vol 321 ◽

pp. 1-17 ◽

Author(s):

Hyun Geun Lee ◽

Jaemin Shin ◽

June-Yub Lee

Keyword(s):

Phase Field ◽

Second Order ◽

Order Energy ◽

Energy Stable ◽

Phase Field Crystal

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A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q-tensor model of liquid crystals

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2017.01.031 ◽

2017 ◽

Vol 318 ◽

pp. 803-825 ◽

Author(s):

Jia Zhao ◽

Xiaofeng Yang ◽

Yuezheng Gong ◽

Qi Wang

Keyword(s):

Liquid Crystals ◽

Second Order ◽

Tensor Model ◽

Energy Stable ◽

Energy Stable Scheme ◽

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Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

Journal of Computational Physics ◽

10.1016/j.jcp.2016.10.020 ◽

2017 ◽

Vol 330 ◽

pp. 1116-1134 ◽

Author(s):

Xiaofeng Yang ◽

Daozhi Han

Keyword(s):

Phase Field ◽

Second Order ◽

Crystal Model ◽

Energy Stable Schemes ◽

Energy Stable ◽

Phase Field Crystal

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Linear, Second-Order Accurate, and Energy Stable Scheme for a Ternary Cahn–Hilliard Model by Using Lagrange Multiplier Approach

Acta Applicandae Mathematicae ◽

10.1007/s10440-021-00405-6 ◽

2021 ◽

Vol 172 (1) ◽

Author(s):

Junxiang Yang ◽

Junseok Kim

Keyword(s):

Lagrange Multiplier ◽

Second Order ◽

Energy Stable ◽

Energy Stable Scheme ◽

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