[1]
|
Cahn, J. and Hilliard, J. (1958) Free Energy of a Nonuniform System. I. Interfacial Free Energy. The Journal of Chemical Physics, 28, 258-267. https://doi.org/10.1063/1.1744102
|
[2]
|
Karma, A. and Rappel, W.J. (1998) Quantitative Phase-Field Modeling of Dendritic Growth in Two and Three Dimensions. Physical Review E, 57, 4323-4349. https://doi.org/10.1103/PhysRevE.57.4323
|
[3]
|
Allen, S. and Cahn, J. (1979) A Microscopic Theory for Antiphase Boundary Motion and Its Application to Antiphase Domain Coarsening. Acta Materialia, 27, 1085-1095. https://doi.org/10.1016/0001-6160(79)90196-2
|
[4]
|
Kobayashi, R. (1993) Modeling and Numerical Simulations of Dendritic Crystal Growth. Phys- ica D: Nonlinear Phenomena, 63, 410-423. https://doi.org/10.1016/0167-2789(93)90120-P
|
[5]
|
Gurtin, M., Polignone, D. and Vinals, J. (1996) Two-Phase Binary Fluids and Immiscible Flu- ids Described by an Order Parameter. Mathematical Models and Methods in Applied Sciences, 6, 815-831. https://doi.org/10.1142/S0218202596000341
|
[6]
|
Barret, J., Blowey, J. and Garcke, H. (1999) Finite Element Approximation of the Cahn- Hilliard Equation with Degenerate Mobility. SIAM Journal on Numerical Analysis, 37, 286- 318. https://doi.org/10.1137/S0036142997331669
|
[7]
|
Elliott, C. and French, D. (1989) A Nonconforming Finite-Element Method for the Two- Dimensional Cahn-Hilliard Equation. SIAM Journal on Numerical Analysis, 26, 884-903. https://doi.org/10.1137/0726049
|
[8]
|
Elliott, C. and French, D. (1987) Numerical Studies of the Cahn-Hilliard Equation for Phase Separation. IMA Journal of Applied Mathematics, 38, 97-128. https://doi.org/10.1093/imamat/38.2.97
|
[9]
|
Shen, J., Xu, J. and Yang, J. (2018) The Scalar Auxiliary Variable (SAV) Approach for Gradient Flows. Journal of Computational Physics, 353, 407-416. https://doi.org/10.1016/j.jcp.2017.10.021
|
[10]
|
Zhao, S., Xiao, X. and Feng, X. (2020) An Efficient Time Adaptivity Based on Chemical Potential for Surface Cahn-Hilliard Equation Using Finite Element Approximation. Applied Mathematics and Computation, 369, Article ID: 124901. https://doi.org/10.1016/j.amc.2019.124901
|
[11]
|
Mao, D., Shen, L. and Zhou, A. (2006) Adaptive Finite Element Algorithms for Eigenvalue Problems Based on Local Averaging Type a Posteriori Error Estimates. Advances in Compu- tational Mathematics, 25, 135-160. https://doi.org/10.1007/s10444-004-7617-0
|
[12]
|
Chen, Y., Huang, Y. and Yi, N. (2021) A Decoupled Energy Stable Adaptive Finite Ele- ment Method for Cahn-Hilliard-Navier-Stokes Equations. Communications in Computational Physics, 29, 1186-1212. https://doi.org/10.4208/cicp.OA-2020-0032
|
[13]
|
Zhang, Z. and Qiao, Z. (2012) An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation. Communications in Computational Physics, 11, 1261-1278. https://doi.org/10.4208/cicp.300810.140411s
|
[14]
|
Huang, Y. and Yi, N. (2010) The Superconvergent Cluster Recovery Method. Journal of Sci- entific Computing, 44, 301-322. https://doi.org/10.1007/s10915-010-9379-9
|
[15]
|
Chen, Y., Huang, Y. and Yi, N. (2019) A SCR-Based Error Estimation and Adaptive Finite Element Method for the Allen-Cahn Equation. Computers and Mathematics with Applications, 78, 204-223. https://doi.org/10.1016/j.camwa.2019.02.022
|
[16]
|
Guillen-Gonzalez, F. and Tierra, G. (2014) Second Order Schemes and Time-Step Adaptivity for Allen-Cahn and Cahn-Hilliard Models. Computers and Mathematics with Applications, 68, 821-846. https://doi.org/10.1016/j.camwa.2014.07.014
|
[17]
|
Feng, X. and Prohl, A. (2004) Error Analysis of a Mixed Finite Element Method for the Cahn- Hilliard Equation. Numerische Mathematik, 99, 47-84. https://doi.org/10.1007/s00211-004-0546-5
|
[18]
|
Shen, J. and Yang, X. (2010) Numerical Approximations of Allen-Cahn and Cahn-Hilliard Equations. Discrete and Continuous Dynamical Systems, 28, 1669-1691. https://doi.org/10.3934/dcds.2010.28.1669
|
[19]
|
Li, C., Huang, Y. and Yi, N. (2019) An Unconditionally Energy Stable Second Order Finite Element Method for Solving the Allen-Cahn Equation. Journal of Computational and Applied Mathematics, 353, 38-48. https://doi.org/10.1016/j.cam.2018.12.024
|