Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model (Record no. 703)

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fixed length control field 01424nam a2200169 a 4500
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control field 20260901030408.0
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fixed length control field 250101s2020 xx o 000 0 eng d
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Juan Zhang
245 10 - TITLE STATEMENT
Title Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model
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Name of producer, publisher, distributor, manufacturer arXiv
Date of production, publication, distribution, manufacture, or copyright notice 2020
336 ## - CONTENT TYPE
Content type term text
338 ## - CARRIER TYPE
Carrier type term online resource
520 ## - SUMMARY, ETC.
Summary, etc. In this paper, two finite difference numerical schemes are proposed and analyzed for the droplet liquid film model, with a singular Leonard-Jones energy potential involved. Both first and second order accurate temporal algorithms are considered. In the first order scheme, the convex potential and the surface diffusion terms are implicitly, while the concave potential term is updated explicitly. Furthermore, we provide a theoretical justification that this numerical algorithm has a unique solution, such that the positivity is always preserved for the phase variable at a point-wise level, so that a singularity is avoided in the scheme. In fact, the singular nature of the Leonard-Jones potential term around the value of 0 prevents the numerical solution reaching such singular value, so that the positivity structure is always preserved. Moreover, an unconditional energy stability of the nume
506 0# - RESTRICTIONS ON ACCESS NOTE
Terms governing access Open access — freely available to read.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://arxiv.org/pdf/2012.11802v1">https://arxiv.org/pdf/2012.11802v1</a>
Link text Read the full paper (PDF)
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      Available online General Yegates University Library Yegates University Library Science and Computing 09/01/2026   YGE000964 09/01/2026 https://arxiv.org/pdf/2012.11802v1 09/01/2026 Research paper — read online