Finite element analysis of a nonlinear parabolic equation modeling epitaxial thin-film growth
Tóm tắt
Từ khóa
Tài liệu tham khảo
Barrett JW, Blowey JF, Garcke H: Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. SIAM J. Numer. Anal. 1999, 37: 286-318. 10.1137/S0036142997331669
Choo SM, Kim YH: Finite element scheme for the viscous Cahn-Hilliard equation with a nonconstant gradient energy coefficient. J. Appl. Math. Comput. 2005, 19: 385-395. 10.1007/BF02935813
Elliott CM, French DA: A nonconforming finite element method for the two-dimensional Cahn-Hilliard equation. SIAM J. Numer. Anal. 1989, 26: 884-903. 10.1137/0726049
Feng X, Wu H: A posteriori error estimates for finite element approximations of the Cahn-Hilliard equation and the Hele-Shaw flow. J. Comput. Math. 2008, 26: 767-796.
Kovács M, Larsson S, Mesforush A: Finite element approximation of the Cahn-Hilliard-Cook equation. SIAM J. Numer. Anal. 2011, 49: 2407-2429. 10.1137/110828150
Zhang T: Finite element analysis for Cahn-Hilliard equation. Math. Numer. Sin. 2006, 28: 281-292.
King BB, Stein O, Winkler M: A fourth order parabolic equation modeling epitaxial thin film growth. J. Math. Anal. Appl. 2003, 286: 459-490. 10.1016/S0022-247X(03)00474-8
Zangwill A: Some causes and a consequence of epitaxial roughening. J. Cryst. Growth 1996, 163: 8-21. 10.1016/0022-0248(95)01048-3
Kohn RV, Yan X: Upper bound on the coarsening rate for an epitaxial growth model. Commun. Pure Appl. Math. 2003, 56: 1549-1564. 10.1002/cpa.10103
Liu C: Regularity of solutions for a fourth order parabolic equation. Bull. Belg. Math. Soc. Simon Stevin 2006, 13(3):527-535.
Zhao X, Liu C: The existence of global attractor for a fourth-order parabolic equation. Appl. Anal. 2013, 92: 44-59. 10.1080/00036811.2011.590476
Zhao X, Liu C: Optimal control of a fourth-order parabolic equation modeling epitaxial thin-film growth. Bull. Belg. Math. Soc. Simon Stevin 2013, 20(3):547-557.
Ciarlet P: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam; 1978.