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math.NA2026
Energy-Dissipative, High-Order BDF Schemes for Simulating Geometric Flows via Energy Increments
Zhiqing Pan, Wei Jiang, Jiwei Jia
We propose energy-dissipative backward differentiation formula (BDF) methods for geometric flows in the Barrett--Garcke--Nürnberg (BGN) parametric finite element framework. Startin…
math.NA2026
Second-Order Area/Volume-Preserving PFEMs for Surface Diffusion via Simpson--Boole Geometric Identities
Zhiqing Pan, Jiwei Jia, Lian Zhang
We propose second-order-in-time parametric finite element methods for surface diffusion of closed curves in two dimensions and closed surfaces in three dimensions. The construction…