147 citations · 339 across the 50 of their papers we have counts for
51 papers
Why large time-stepping methods for the Cahn-Hilliard equation is stable
Dong Li
We consider the Cahn-Hilliard equation with standard double-well potential. We employ a prototypical class of first order in time semi-implicit methods with implicit treatment of t…
An F-modulated stability framework for multistep methods
Dong Li, Chaoyu Quan, Wen Yang
We introduce a new -modulated energy stability framework for general linear multistep methods. We showcase the theory for the two dimensional molecular beam epitaxy mode…
On the gap property of a linearized NLS operator
Dong Li, Kai Yang
We consider a pair of linear operators corresponding to the linearization around the ground state soliton of the cubic nonlinear Schrödinger equation in dimension three. We introdu…
Remarks on the Bernstein inequality for higher order operators and related results
Dong Li, Yannick Sire
This note is devoted to several results about frequency localized functions and associated Bernstein inequalities for higher order operators. In particular, we construct some count…
Effective maximum principles for spectral methods
Dong Li
Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data, the i…
Negative time splitting is stable
Dong Li, Chaoyu Quan
For high order (than two) in time operator-splitting methods applied to dissipative systems, a folklore issue is the appearance of negative-time/backward-in-time linear evolution o…