Mathematics > Numerical Analysis
arXiv:2405.05844 (math)
[Submitted on 9 May 2024 (v1), last revised 27 May 2024 (this version, v2)]
Title:Structure-preserving parametric finite element methods for simulating axisymmetric solid-state dewetting problems with anisotropic surface energies
View a PDF of the paper titled Structure-preserving parametric finite element methods for simulating axisymmetric solid-state dewetting problems with anisotropic surface energies, by Meng Li and 1 other authors
View PDFHTML (experimental)Abstract:Solid-state dewetting (SSD), a widespread phenomenon in solid-solid-vapor system, could be used to describe the accumulation of solid thin films on the substrate. In this work, we consider the sharp interface model for axisymmetric SSD with anisotropic surface energy. By introducing two types of surface energy matrices from the anisotropy functions,we aim to design two structure-preserving algorithms for the axisymmetric SSD. The newly designed schemes are applicable to a broader range of anisotropy functions, and we can theoretically prove their volume conservation and energy stability. In addition, based on a novel weak formulation for the axisymmetric SSD, we further build another two numerical schemes that have good mesh properties. Finally, numerous numerical tests are reported to showcase the accuracy and efficiency of the numerical methods.
| Subjects: | Numerical Analysis (math.NA) |
| Cite as: | arXiv:2405.05844 [math.NA] |
| (orarXiv:2405.05844v2 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2405.05844 arXiv-issued DOI via DataCite |
Submission history
From: Meng Li [view email][v1] Thu, 9 May 2024 15:30:11 UTC (475 KB)
[v2] Mon, 27 May 2024 05:13:28 UTC (787 KB)
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View a PDF of the paper titled Structure-preserving parametric finite element methods for simulating axisymmetric solid-state dewetting problems with anisotropic surface energies, by Meng Li and 1 other authors
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