An Unconditionally Gradient Stable Adaptive Mesh Refinement for the Cahn-Hilliard Equation

Kim, Jun-Seok;Bae, Hyeong-Ohk

  • Published : 20080000

Abstract

Keywords

References

  1. J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 28, 258 (1958) https://doi.org/10.1063/1.1744102
  2. C. M. Elliott and D. A. French, IMA J. Appl. Math. 38, 97 (1987) https://doi.org/10.1093/imamat/38.2.97
  3. J. S. Kim, Appl. Math. Comput. 160, 589 (2005) https://doi.org/10.1016/j.amc.2003.11.020
  4. J. S. Kim, J. Comput. Phys. 204, 784 (2005) https://doi.org/10.1016/j.jcp.2004.10.032
  5. J. S. Kim and J. S. Lowengrub, Interfaces Free Bound. 7, 435 (2005)
  6. J. S. Kim, K. K. Kang and J. S. Lowengrub, J. Comput. Phys. 193, 511 (2004) https://doi.org/10.1016/j.jcp.2003.07.035
  7. H. Garcke, T. Preusser, M. Rumpf, A. C. Telea, U. Weokard and J. J. van Wijk, IEEE TVCG 7, 230 (2001)
  8. A. Bertozzi, S. Esedoglu and A. Gillette, IEEE Trans. Image Proc. 16, 285 (2007) https://doi.org/10.1109/TIP.2006.887728
  9. J. Y. Kim, J. K. Yoon and P. R. Cha, J. Korean Phys. Soc. 49, 1501 (2006)
  10. S. M. Wise, J. S. Lowengrub, J. S. Kim, K. Thornton, P. W. Voorhees and W. C. Johnson, Appl. Phys. Lett. 87, 133102-1 (2005) https://doi.org/10.1063/1.2061852
  11. B. H. Koo, G. B. Chon, H. S. Lim, C. G. Lee and T. Yao, J. Korean Phys. Soc. 49, 873 (2006)
  12. S. H. Hwang, D. W. Kwon, J. D. Song, W. J. Choi and J. I. LEE, J. Korean Phys. Soc. 51, 262 (2007) https://doi.org/10.3938/jkps.51.262
  13. E. V. L. Melloa and O. T. S. Filho, Physica A 347, 429 (2005) https://doi.org/10.1016/j.physa.2004.08.076
  14. D. J. Eyre, http://www.math.utah.edu/eyre/research/methods/stable.ps
  15. D. J. Eyre, Computational and Mathematical Models of Microstructural Evolution (The Material Research Society, Warrendale, 1998), p. 39
  16. C. Cowan, M.S. Thesis, Simon Fraser University, Canada, 2005
  17. P. C. Fife, E. J. Di. Eqns. 48, 1 (2000)
  18. J. W. Cahn, Acta Metallurgica 9, 795 (1961) https://doi.org/10.1016/0001-6160(61)90182-1
  19. J. W. Cahn and J. H. Hilliard, Acta Metall. 19, 151 (1971) https://doi.org/10.1016/0001-6160(71)90127-1
  20. S. Agmon, A. Douglis and L. Nirenberg, Comm. Pure Appl. Math. 17, 35 (1964) https://doi.org/10.1002/cpa.3160170104
  21. S. Agmon, A. Douglis and L. Nirenberg, Comm. Pure Appl. Math. 12, 623 (1959) https://doi.org/10.1002/cpa.3160120405
  22. D. Gilbarg and N. S. Trudinger, Classics in Mathematics (Springer-Verlag, Berlin, 2001)
  23. J. Greer, A. Bertozzi and G. Sapiro, J. Comput. Phys. 216, 216 (2006) https://doi.org/10.1016/j.jcp.2005.11.031
  24. A. Miranville, J. Appl. Math. 4, 165 (2003)
  25. J. S. Kim, J. Korean Phys. Soc. 49, 1903 (2006)
  26. S. M. Wise, J. S. Kim and J. S. Lowengrub, J. Comput. Phys. 226, 414 (2007) https://doi.org/10.1016/j.jcp.2007.04.020
  27. S. J. Lee, J. O. Kim, S. K. Noh and K.-S. Lee, J. Korean Phys. Soc. 51, 1027 (2007) https://doi.org/10.3938/jkps.51.1027
  28. J. Nah and E. K. Kim, J. Korean Phys. Soc. 51, 1362 (2007) https://doi.org/10.3938/jkps.51.1362
  29. J. S. Kim, E. K. Kim, H. J. Kim and E. Yoon, J. Korean Phys. Soc. 51, 1195 (2007) https://doi.org/10.3938/jkps.51.1195