Bänsch E, Haußer F, Voigt A (2005)
Publication Type: Journal article, Original article
Publication year: 2005
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 26
Pages Range: 2029-2046
Journal Issue: 6
DOI: 10.1137/030601028
We develop an adaptive finite element method for island dynamics in epitaxial growth. We study a step-flow model, which consists of an adatom (adsorbed atom) diffusion equation on terraces of different height; thermodynamic boundary conditions on terrace boundaries including anisotropic line tension; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional anisotropic "surface" diffusion (edge diffusion) of edge adatoms along the step edges. The problem is solved using independent meshes: a two-dimensional mesh for the adatom diffusion and one-dimensional meshes for the boundary evolution. A penalty method is used to incorporate the boundary conditions. The evolution of the terrace boundaries includes both the weighted/anisotropic mean curvature flow and the weighted/anisotropic edge diffusion. Its governing equation is solved by a semi-implicit front-tracking method using parametric finite elements. © 2005 Society for Industrial and Applied Mathematics.
APA:
Bänsch, E., Haußer, F., & Voigt, A. (2005). Finite element method for epitaxial growth with thermodynamic boundary conditions. SIAM Journal on Scientific Computing, 26(6), 2029-2046. https://doi.org/10.1137/030601028
MLA:
Bänsch, Eberhard, Frank Haußer, and Axel Voigt. "Finite element method for epitaxial growth with thermodynamic boundary conditions." SIAM Journal on Scientific Computing 26.6 (2005): 2029-2046.
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