65 citations · 188 across the 26 of their papers we have counts for
13 papers · 1 filter
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…
Energy Stable L2 Schemes for Time-Fractional Phase-Field Equations
Chaoyu Quan, Boyi Wang
In this article, the energy stability of two high-order L2 schemes for time-fractional phase-field equations is established. We propose a reformulation of the L2 operator and also…
Stability and convergence of Strang splitting. Part II: tensorial Allen-Cahn equations
Dong Li, Chaoyu Quan, Jiao Xu
We consider the second-order in time Strang-splitting approximation for vector-valued and matrix-valued Allen-Cahn equations. Both the linear propagator and the nonlinear propagato…
Stability and convergence of Strang splitting. Part I: Scalar Allen-Cahn equation
Dong Li, Chaoyu Quan, Jiao Xu
We consider a class of second-order Strang splitting methods for Allen-Cahn equations with polynomial or logarithmic nonlinearities. For the polynomial case both the linear and the…
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…
On a sinc-type MBE model
Xinyu Cheng, Dong Li, Chaoyu Quan +1
We introduce a new sinc-type molecular beam epitaxy model which is derived from a cosine-type energy functional. The landscape of the new functional is remarkably similar to the cl…
Energy-dissipation for time-fractional phase-field equations
Dong Li, Chaoyu Quan, Jiao Xu
We consider a class of time-fractional phase field models including the Allen-Cahn and Cahn-Hilliard equations. We establish several weighted positivity results for functionals dri…
Sharp convergence to steady states of Allen-Cahn
Dong Li, Chaoyu Quan, Tao Tang +1
In our recent work we found a surprising breakdown of symmetry conservation: using standard numerical discretization with very high precision the computed numerical solutions corre…
On symmetry breaking of Allen-Cahn
Dong Li, Chaoyu Quan, Tao Tang +1
We consider numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numer…
On a parabolic sine-Gordon model
Xinyu Cheng, Dong Li, Chaoyu Quan +1
We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the o…
The BDF3/EP3 scheme for MBE with no slope selection is stable
Dong Li, Chaoyu Quan, Wen Yang
We consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. We employ a third order backward differentiation (BDF3) in…