3 papers
math.NA2026
High-order energy-stable BGN parametric finite element methods for geometric flows
Shu Ma, Qiqi Rao
We construct high-order Runge--Kutta extensions of Barrett--Garcke--Nürnberg (BGN) parametric finite element methods for curve-shortening flow and curve diffusion of planar curves…
math.NA2026
B-spline-Based ALE-MFS Framework for Evolving Domains
Muhammad Ammad, Leevan Ling, Shu Ma
We develop and analyze a B-spline based arbitrary Lagrangian-Eulerian method of fundamental solutions (ALE-MFS) for curvature-driven motion of two-dimensional evolving domains. Bou…
math.NA2025
Optimal convergence of the arbitrary Lagrangian-Eulerian interface tracking method for two-phase Navier--Stokes flow without surface tension
Buyang Li, Shu Ma, Weifeng Qiu
Optimal-order convergence in the norm is proved for an arbitrary Lagrangian-Eulerian interface tracking finite element method for the sharp interface model of two-phase Navie…