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math.NA2026
UnCut FEM with PHT-splines on unfitted T-meshes
Falai Chen, Nuo Lei, Buyang Li
We propose a novel unfitted finite element method based on polynomial splines over hierarchical T-meshes (PHT-splines) for elliptic partial differential equations (PDEs) posed on d…
math.NA2026
An energy--stable ALE--FEM with compensated tangential velocity for Navier--Stokes free--boundary flows
Nuo Lei, Weiying Zheng, Na Zhu
We propose an energy-stable arbitrary Lagrangian-Eulerian (ALE) finite element formulation for incompressible Navier-Stokes flows with surface-tension-driven free boundaries. The k…
math.NA2026
A structure--preserving ALE--BGN--MDR method for Navier--Stokes free boundary problems with moving contact lines and gravity
Harald Garcke, Jiashun Hu, Nuo Lei
We propose a gravity-consistent arbitrary Lagrangian--Eulerian finite element method for incompressible Navier--Stokes free-boundary problems with moving contact lines. A direct bo…