A $θ-L$ Formulation-Based Finite Element Method for Solving Axisymmetric Solid-State Dewetting Problems
Year: 2021
Author: Weijie Huang, Wei Jiang, Quan Zhao
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 389–405
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.130920.071220
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 389–405
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Solid-state dewetting surface diffusion moving contact line $θ-L$ formulation finite element method.