A parametric finite element method for solid-state dewetting problems with anisotropic surface energies
arXiv:1601.05877 · doi:10.1016/j.jcp.2016.11.015
Abstract
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.
24 pages, 15 figures
References in corpus (4)
- Sharp interface model for solid-state dewetting problems with weakly anisotropic surface energies
- Degenerate Mobilities in Phase Field Models are Insufficient to Capture Surface Diffusion
- On the stable discretization of strongly anisotropic phase field models with applications to crystal growth
- Stable Equilibria of Anisotropic Particles on Substrates: a Generalized Winterbottom Construction
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- Controlling fingering instabilities in Hele-Shaw flows in the presence of wetting film effects
- An Energy-stable Finite Element Method for the Simulation of Moving Contact Lines in Two-phase Flows
- Solid-state dewetting on curved substrates
- Doubly Degenerate Diffuse Interface Models of Anisotropic Surface Diffusion
- An energy-stable parametric finite element method for simulating solid-state dewetting
- Sharp-interface model for simulating solid-state dewetting in three dimensions
- An Energy-Stable Parametric Finite Element Method for Simulating Solid-state Dewetting Problems in Three Dimensions
- Phase-field Modelling of Anisotropic Solid-State Dewetting on Patterned Substrates