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An energy-stable parametric finite element framework for surface diffusion with moving contact lines on curved substrates
Abstract
We develop energy-stable parametric finite element methods for surface diffusion of solid films with moving contact lines on curved substrates. Discretizing both the film surface and the substrate patches allows the introduction of linear schemes that are unconditionally energy stable. A nonlinear variant of the schemes ensures that, in addition, the vertices of the substrate approximations remain attached to the true substrate throughout. Moreover, our framework can incorporate anisotropic surface energy densities, for both the film surface and the substrate, as well as different tangential motions. Numerical experiments in two and three space dimensions illustrate the practicality of the introduced methods.
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BibTeX
@misc{garcke2026energystable,
title = {{An energy-stable parametric finite element framework for surface diffusion with moving contact lines on curved substrates}},
author = {Harald Garcke and Robert Nürnberg and Rong Tang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32270},
eprint = {2610.32270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32270},
}
RIS
TY - UNPB
TI - An energy-stable parametric finite element framework for surface diffusion with moving contact lines on curved substrates
AU - Harald Garcke
AU - Robert Nürnberg
AU - Rong Tang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32270
UR - https://arxiv.org/abs/2610.32270
AB - We develop energy-stable parametric finite element methods for surface diffusion of solid films with moving contact lines on curved substrates. Discretizing both the film surface and the substrate patches allows the introduction of linear schemes that are unconditionally energy stable. A nonlinear variant of the schemes ensures that, in addition, the vertices of the substrate approximations remain attached to the true substrate throughout. Moreover, our framework can incorporate anisotropic surface energy densities, for both the film surface and the substrate, as well as different tangential motions. Numerical experiments in two and three space dimensions illustrate the practicality of the introduced methods.
ER -