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Adaptive moving mesh methods for the planar Willmore flow
Zhenghua Duan, Meng Li
In this paper, we propose adaptive moving mesh methods for the planar Willmore flow by incorporating a tangential velocity into the original geometric evolution. The tangential vel…
Structure-preserving parametric finite element methods for anisotropic surface diffusion flow with minimal deformation formulation
Yihang Guo, Meng Li
High mesh quality plays a crucial role in maintaining the stability of solutions in geometric flow problems. Duan and Li [Duan & Li, SIAM J. Sci. Comput. 46 (1) (2024) A587-A608] a…
Efficient energy-stable parametric finite element methods for surface diffusion flow and applications in solid-state dewetting
Meng Li, Yihang Guo, Jingjiang Bi
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-…
Structure-preserving weighted BDF2 methods for Anisotropic Cahn-Hilliard model: uniform/variable-time-steps
Meng Li, Jingjiang Bi, Nan Wang
In this paper, we innovatively develop uniform/variable-time-step weighted and shifted BDF2 (WSBDF2) methods for the anisotropic Cahn-Hilliard (CH) model, combining the scalar auxi…