"Unconditionally Stable Schemes for Equations of Thin Film Epitaxy" by Cheng Wang, Xiaoming Wang et al.
 

Unconditionally Stable Schemes for Equations of Thin Film Epitaxy

Abstract

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Convexity Splitting; Energy Stability; Epitaxial Growth; Long-Time Stability

International Standard Serial Number (ISSN)

1078-0947

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Sep 2010

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