Unconditionally Stable Schemes for Equations of Thin Film Epitaxy
We present unconditionally stable and convergent numerical schemes for gradient flows with energy of the form √ (F(Δφ(x)) +ε2/2|Δ(x)|2) dx. the construction of the schemes involves an appropriate extension of Eyre's idea of convex-concave decomposition of the energy functional. as an application, we derive unconditionally stable and convergent schemes for epitaxial film growth models with slope selection (F (y) = 1/4(|y|2 - 1)2) and without slope selection (F (y) = - 1/21n(1 + |y|2 )). We conclude the paper with some preliminary computations that employ the proposed schemes.
C. Wang et al., "Unconditionally Stable Schemes for Equations of Thin Film Epitaxy," Discrete and Continuous Dynamical Systems, vol. 28, no. 1, pp. 405 - 423, American Institute of Mathematical Sciences (AIMS), Sep 2010.
The definitive version is available at https://doi.org/10.3934/dcds.2010.28.405
Mathematics and Statistics
Keywords and Phrases
Convexity Splitting; Energy Stability; Epitaxial Growth; Long-Time Stability
International Standard Serial Number (ISSN)
Article - Journal
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01 Sep 2010