Juan Zhang creator text xx 2020 monographic ng

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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 Open access — freely available to read. https://arxiv.org/pdf/2012.11802v1 https://arxiv.org/pdf/2012.11802v1 Open access — freely available to read. 250101 20260901030408.0