Approximation and application of minimizing movements for surface PDE
<|reference_start|>Approximation and application of minimizing movements for surface PDE: By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then used to develop threshold dynamics algorithms for surface-constrained interfacial motions. In particular, show how the minimizing movements enable one to approximate multiphase, volume-preserving, curvature flows on surfaces via generalized MBO and HMBO algorithms.<|reference_end|>
@article{ginder2024approximation,
    title={Approximation and application of minimizing movements for surface PDE},
    author={Elliott Ginder, Karel Svadlenka, Takuma Muramatsu},
    journal={arXiv preprint arXiv:2409.03139},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03139},
    primaryClass={math.NA cs.NA}
}