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A Discrete Scheme for Parametric Anisotropic Surface Diffusion

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Abstract

In this note we present, how anisotropic surface energies may be incorporated into the finite element method for parametric surface diffusion given by Bänsch et al. [2004. J. Comput. Phys. 203, 321–343]. We present the adapted variational formulation, and the resulting semi-implicit discretization. Finally several simulations with strong (convex) anisotropies are shown, where the corresponding Wulff shapes are approached as the steady state

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References

  1. Bänsch E., Morin P., and Nochetto R.H. (2005). A finite element method for surface diffusion: the parametric case. J. Comput. Phys. 203:321–343

    Article  MATH  MathSciNet  Google Scholar 

  2. Bänsch E., Haußer F., Lakkis O., Li B., and Voigt A. (2004). Finite element method for epitaxial growth with attachment-detachment kinetics. J. Comput. Phys. 194:409–434

    Article  MATH  MathSciNet  Google Scholar 

  3. Cahn J.W., and Hoffman D.W. (1974). Vector thermodynamics for anisotropic surfaces 2. curved and faceted surfaces. Acta Metall. 22:1205–1214

    Article  Google Scholar 

  4. Clarenz U., Dziuk G., and Rumpf M. (2003). On generalized mean curvature flow in surface processing. In Geometric Analysis and Nonlinear Partial Differential Equations. Springer, Berlin, pp. 217–248

    Google Scholar 

  5. Deckelnick, K., Dziuk, G., and Elliott, C. M. (2005). Computation of geometric partial differential equations and mean curvature flow. Acta Numerica

  6. Deckelnick K., Dziuk G., and Elliott C.M. (2005). Fully discrete finite element approximation for anisotropic surface diffusion of graphs. SIAM J. Numer. Anal. 43(3):1112–1138

    Article  MathSciNet  MATH  Google Scholar 

  7. Dziuk G. (1991). An algorithm for evolutionary surfaces. Numer. Math. 58:603–611

    Article  MATH  MathSciNet  Google Scholar 

  8. Mullins W.W. (1957). Theory of thermal grooving. J. Appl. Phys. 28(3):333–339

    Article  Google Scholar 

  9. Taylor J.E. (1978). Crystalline variational problems. Bull. Amer. Math. Soc. 84(4):568–588

    Article  MATH  MathSciNet  Google Scholar 

  10. Taylor J.E. (1992). Mean curvature and weighted mean curvature. Acta Metall. Mater. 40(7):1475–1485

    Article  Google Scholar 

  11. Vey S., and Voigt A. (2004). AMDiS – adaptive multidimensional simulations: object oriented software concepts for scientific computing. WSEAS Transac. Syst. 3:1564–1569

    Google Scholar 

  12. Wulff G. (1901). Zur Frage der Geschwindigkeit des Wachstums und der Auflösung der Kristallflächen. Zeitschr. F. Kristallog. 34:449–530

    Google Scholar 

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  1. Crystal Growth Group, Research center caesar, Ludwig-Erhard-Allee 2, Bonn, 53175, Germany

    Frank Haußer & Axel Voigt

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  1. Frank Haußer
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  2. Axel Voigt
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Correspondence to Frank Haußer.

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Haußer, F., Voigt, A. A Discrete Scheme for Parametric Anisotropic Surface Diffusion. J Sci Comput 30, 223–235 (2007). https://doi.org/10.1007/s10915-005-9064-6

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  • DOI: https://doi.org/10.1007/s10915-005-9064-6

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