18 citations · 85 across the 30 of their papers we have counts for
9 papers · 2 filters
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…
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…
On the energy stability of Strang-splitting for Cahn-Hilliard
Dong Li, Chaoyu Quan
We consider a Strang-type second order operator-splitting discretization for the Cahn-Hilliard equation. We introduce a new theoretical framework and prove uniform energy stability…
The operator-splitting method for Cahn-Hilliard is stable
Dong Li, Chaoyu Quan
We prove energy stability of a standard operator-splitting method for the Cahn-Hilliard equation. We establish uniform bound of Sobolev norms of the numerical solution and converge…