  In this work, we aim to develop energy-stable parametric finite element
approximations for a sharp-interface model with strong surface energy
anisotropy, which is derived from the first variation of an energy functional
composed of film/vapor interfacial energy, substrate energy, and regularized
Willmore energy. By introducing two geometric relations, we innovatively
establish an equivalent regularized sharp-interface model and further construct
an energy-stable parametric finite element algorithm for this equivalent model.
We provide a detailed proof of the energy stability of the numerical scheme,
addressing a gap in the relevant theory. Additionally, we develop another
structure-preserving parametric finite element scheme that can preserve both
area conservation and energy stability. Finally, we present several numerical
simulations to show accuracy and efficiency as well as some
structure-preserving properties of the proposed numerical methods. More
importantly, extensive numerical simulations reveal that our schemes provide
better mesh quality and are more suitable for long-term computations.
