5 papers
A second-order energy-stable low-regularity integrator for the Navier--Stokes equations
Shu Ma
A second-order exponential low-regularity integrator is proposed for the incompressible Navier--Stokes equations. The method requires only linear solves and satisfies a discrete en…
High-order energy diminishing ALE-SAV finite element methods for two-phase Navier--Stokes flow
Shu Ma
We develop a high-order fully discrete ALE-SAV finite element method for sharp-interface two-phase Navier--Stokes flow that satisfies a discrete energy dissipation law. We introduc…
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…
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…
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…