Our latest work Phase-field computation for 3D shell reconstruction with an energy-stable and uniquely solvable BDF2 method has been published to CMA recently.

The algorithm uses a linearized backward differentiation formula (BDF2) for time advancement and adopts the finite difference method to perform spatial discretization, unconditional energy stability and second order time accuracy can be achieved. The present method is not only suitable for 3D reconstruction of unordered data but also has the effect of adaptive denoising and surface smoothing. In addition, theoretical derivation proves the fully discrete energy stability.

If you are interested in our work, please kindly follow the link below:
https://www.sciencedirect.com/science/article/pii/S0898122125001166