@Article{EAJAM-11-389,
author = {Huang , WeijieJiang , Wei and Zhao , Quan},
title = {A $θ-L$ Formulation-Based Finite Element Method for Solving Axisymmetric Solid-State Dewetting Problems},
journal = {East Asian Journal on Applied Mathematics},
year = {2021},
volume = {11},
number = {2},
pages = {389--405},
abstract = {<p style="text-align: justify;">We propose a $θ-L$ formulation-based finite element method for the sharp-interface model of solid-state dewetting with axisymmetric geometry. The model describes the film/vapor interface using the radial curve in cylindrical coordinates, and is
governed by a fourth-order geometric partial differential equation with complex boundary conditions at the moving contact lines. By introducing an appropriate tangential
velocity, we derive an equivalent system for the original sharp-interface model. This
gives the kinetic equation for the tangential angle $θ$ and the total length $L$ of the radial curve. The new formulation can alleviate the stiffness of the original model and
help to maintain mesh equidistribution during the evolution. We present an efficient
finite element method for solving the resulting $θ-L$ formulation based on its weak form.
Numerical examples are reported to demonstrate the accuracy and efficiency of the numerical scheme.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.130920.071220 },
url = {http://global-sci.org/intro/article_detail/eajam/18640.html}
}