Finite element approximation of a three dimensional phase field model for void electromigration

Journal of Scientific Computing

Volumn 37, Issue 2, 2008, Pages 202-232

  Baňas, L'ubomír ^a,b   Nürnberg, Robert ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Convergence analysis; Degenerate Cahn Hilliard equation; Finite elements; Fourth order degenerate parabolic system; Multigrid methods; Phase field model; Surface diffusion; Void electromigration

Indexed keywords

CONVERGENCE ANALYSIS; DEGENERATE CAHN-HILLIARD EQUATION; FINITE ELEMENTS; FOURTH ORDER DEGENERATE PARABOLIC SYSTEM; MULTIGRID METHODS; PHASE FIELD MODEL; VOID ELECTROMIGRATION;

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; CRACKS; DIFFUSION IN SOLIDS; ELECTROMIGRATION; FEATURE EXTRACTION; NON NEWTONIAN FLOW; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; PHASE STABILITY; POLYNOMIAL APPROXIMATION; SEMICONDUCTOR DOPING; SURFACE DIFFUSION; SYSTEM STABILITY; THEOREM PROVING; THREE DIMENSIONAL; TWO DIMENSIONAL; TWO PHASE FLOW;

FINITE ELEMENT METHOD;

EID: 54149105924     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-008-9203-y     Document Type: Article

References (34)

1. Baňas L, Nürnberg R: A multigrid method for the Cahn-Hilliard equation with obstacle potential (2008, submitted)
2. 3. Comput Vis. Sci. 10.1007/s00791-008-0114-0
3. E. Bänsch P. Morin R.H. Nochetto 2005 A finite element method for surface diffusion: the parametric case J. Comput. Phys. 203 321 343
4. J.W. Barrett J.F. Blowey 2001 Finite element approximation of a degenerate Allen-Cahn/Cahn-Hilliard system SIAM J. Numer. Anal. 39 1598 1624
5. J.W. Barrett J.F. Blowey H. Garcke 1998 Finite element approximation of a fourth order nonlinear degenerate parabolic equation Numer. Math. 80 525 556
6. J.W. Barrett J.F. Blowey H. Garcke 1999 Finite element approximation of the Cahn-Hilliard equation with degenerate mobility SIAM J. Numer. Anal. 37 286 318
7. J.W. Barrett J.F. Blowey H. Garcke 2001 On fully practical finite element approximations of degenerate Cahn-Hilliard systems M2AN Math. Model. Numer. Anal. 35 713 748
8. J.W. Barrett S. Langdon R. Nürnberg 2004 Finite element approximation of a sixth order nonlinear degenerate parabolic equation Numer. Math. 96 401 434
9. J.W. Barrett R. Nürnberg V. Styles 2004 Finite element approximation of a phase field model for void electromigration SIAM J. Numer. Anal. 42 738 772
10. J.W. Barrett R. Nürnberg M.R.E. Warner 2006 Finite element approximation of soluble surfactant spreading on a thin film SIAM J. Numer. Anal. 44 1218 1247
11. 3 J. Comput. Phys. 227 4281 4307
12. J.F. Blowey C.M. Elliott 1992 The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. Part II: Numerical analysis Eur. J. Appl. Math. 3 147 179
13. J. Brandts M. Křížek 2003 Gradient superconvergence on uniform simplicial partitions of polytopes IMA J. Numer. Anal. 23 489 505
14. J.W. Cahn C.M. Elliott A. Novick-Cohen 1996 The Cahn-Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature Eur. J. Appl. Math. 7 287 301
15. D.L. Chopp J.A. Sethian 1999 Motion by intrinsic Laplacian of curvature Interfaces Free Bound. 1 107 123
16. K. Deckelnick G. Dziuk C.M. Elliott 2005 Computation of geometric partial differential equations and mean curvature flow Acta Numer. 14 139 232
17. C.M. Elliott H. Garcke 1996 On the Cahn-Hilliard equation with degenerate mobility SIAM J. Math. Anal. 27 404 423
18. X. Feng A. Prohl 2005 Numerical analysis of the Cahn-Hilliard equation and approximation of the Hele-Shaw problem Interfaces Free Bound. 7 1 28
19. Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. Springer, New York (1984)
20. Glowinski, R., Lions, J.-L., Trémolières, R.: Numerical Analysis of Variational Inequalities. Studies in Mathematics and its Applications, vol. 8. North-Holland, Amsterdam (1981). Translated from the French
21. Gräser, C., Kornhuber, R.: On preconditioned Uzawa-type iterations for a saddle point problem with inequality constraints. In: Domain Decomposition Methods in Science and Engineering XVI. Lect. Notes Comput. Sci. Eng., vol. 55, pp. 91-102. Springer, Berlin (2007)
22. G. Grün 2003 On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions Math. Comput. 72 1251 1279
23. R. Kornhuber 1994 Monotone multigrid methods for elliptic variational inequalities I Numer. Math. 69 167 184
24. Z. Li H. Zhao H. Gao 1999 A numerical study of electro-migration voiding by evolving level set functions on a fixed cartesian grid J. Comput. Phys. 152 281 304
25. S. Manservisi 2006 Numerical analysis of Vanka-type solvers for steady stokes and Navier-Stokes flows SIAM J. Numer. Anal. 44 2025 2056
26. U.F. Mayer 2000 A numerical scheme for moving boundary problems that are gradient flows for the area functional Eur. J. Appl. Math. 11 61 80
27. U.F. Mayer 2001 Numerical solutions for the surface diffusion flow in three space dimensions Comput. Appl. Math. 20 361 379
28. W.W. Mullins 1957 Theory of thermal grooving J. Appl. Phys. 28 333 339
29. Nürnberg, R.: Finite element approximation of some degenerate nonlinear parabolic systems. PhD thesis, University of London, London (2003)
30. A. Schmidt K.G. Siebert 2000 ALBERT-software for scientific computations and applications Acta Math. Univ. Comen. (N.S.) 70 105 122
31. J. Schoberl W. Zulehner 2003 On Schwarz-type smoothers for saddle point problems Numer. Math. 95 377 399
32. p (0,T;B) Ann. Math. Pura. Appl. 146 65 96
33. P. Smereka 2003 Semi-implicit level set methods for curvature and surface diffusion motion J. Sci. Comput. 19 439 456
34. Y.W. Zhang A.F. Bower L. Xia C.F. Shih 1999 Three dimensional finite element analysis of the evolution of voids and thin films by strain and electromigration induced surface diffusion J. Mech. Phys. Solids 47 173 199