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math.NA2026
Tangential stability and fully discrete convergence of the classical BGN scheme for curve shortening flow
Qiqi Rao
We prove fully discrete convergence of the classical Barrett--Garcke--Nürnberg (BGN) scheme for curve-shortening flow of smooth embedded closed planar curves. The main obstruction…
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…