376 citations · 2.1k across the 24 of their papers we have counts for
24 papers
Asymptotically compatible energy of variable-step fractional BDF2 formula for time-fractional Cahn-Hilliard model
Hong-lin Liao, Nan Liu, Xuan Zhao
A new discrete energy dissipation law of the variable-step fractional BDF2 (second-order backward differentiation formula) scheme is established for time-fractional Cahn-Hilliard m…
Discrete energy analysis of the third-order variable-step BDF time-stepping for diffusion equations
Hong-lin Liao, Tao Tang, Tao Zhou
This is one of our series works on discrete energy analysis of the variable-step BDF schemes. In this part, we present stability and convergence analysis of the third-order BDF (BD…
Energy stability of variable-step L1-type schemes for time-fractional Cahn-Hilliard model
Bingquan Ji, Xiaohan Zhu, Hong-lin Liao
The positive definiteness of discrete time-fractional derivatives is fundamental to the numerical stability (in the energy sense) for time-fractional phase-field models. A novel te…
Stability of variable-step BDF2 and BDF3 methods
Zhaoyi Li, Hong-lin Liao
We prove that the two-step backward differentiation formula (BDF2) method is stable on arbitrary time grids; while the variable-step BDF3 scheme is stable if almost all adjacent st…
norm error estimates of BDF methods up to fifth-order for the phase field crystal model
Hong-lin Liao, Yuanyuan Kang
The well-known backward difference formulas (BDF) of the third, the fourth and the fifth orders are investigated for time integration of the phase field crystal model. By building…
The variable-step L1 scheme preserving a compatible energy law for time-fractional Allen-Cahn equation
Hong-lin Liao, Xiaohan Zhu, Jindi Wang
In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo's form. The L1 implicit scheme is shown to preserve…
A new discrete energy technique for multi-step backward difference formulas
Honglin Liao, Tao Tang, Tao Zhou
The backward differentiation formula (BDF) is a useful family of implicit methods for the numerical integration of stiff differential equations. It is well noticed that the stabili…
Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn-Hilliard model
Hong-lin Liao, Bingquan Ji, Lin Wang +1
The two-step backward differential formula (BDF2) with unequal time-steps is applied to construct an energy stable convex-splitting scheme for the Cahn-Hilliard model. We focus on…
An energy stable and maximum bound preserving scheme with variable time steps for time fractional Allen-Cahn equation
Hong-lin Liao, Tao Tang, Tao Zhou
In this work, we propose a Crank-Nicolson-type scheme with variable steps for the time fractional Allen-Cahn equation. The proposed scheme is shown to be unconditionally stable (in…
Positive definiteness of real quadratic forms resulting from the variable-step approximation of convolution operators
Hong-lin Liao, Tao Tang, Tao Zhou
The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this…
Analysis of the second order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
Hong-lin Liao, Xuehua Song, Tao Tang +1
In this work, we are concerned with the stability and convergence analysis of the second order BDF (BDF2) scheme with variable steps for the molecular beam epitaxial model without…
An adaptive BDF2 implicit time-stepping method for the phase field crystal model
Hong-lin Liao, Bingquan Ji, Luming Zhang
An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified energy dissipation law at the di…
On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation
Hong-lin Liao, Tao Tang, Tao Zhou
In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is ener…
Analysis of adaptive BDF2 scheme for diffusion equations
Hong-lin Liao, Zhimin Zhang
The variable two-step backward differentiation formula (BDF2) is revisited via a new theoretical framework using the positive semi-definiteness of BDF2 convolution kernels and a cl…
Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint
Bingquan Ji, Hong-lin Liao, Yuezheng Gong +1
A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy sta…
A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
Hong-lin Liao, Tao Tang, Tao Zhou
In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum…
A fourth-order compact solver for fractional-in-time fourth-order diffusion equations
Jialing Zhong, Hong-lin Liao, Bingquan Ji +1
A fourth-order compact scheme is proposed for a fourth-order subdiffusion equation with the first Dirichlet boundary conditions. The fourth-order problem is firstly reduced into a…
Adaptive second-order Crank-Nicolson time-stepping schemes for time fractional molecular beam epitaxial growth models
Bingquan Ji, Hong-lin Liao, Yuezheng Gong +1
Adaptive second-order Crank-Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional Molecular Beam Epitaxial…
Simple maximum-principle preserving time-stepping methods for time-fractional Allen-Cahn equation
Bingquan Ji, Hong-lin Liao, Luming Zhang
Two fast L1 time-stepping methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional Allen-Cahn equation with Caputo's deriva…
Sharp -norm error estimates of two time-stepping schemes for reaction-subdiffusion problems
Jincheng Ren, Hong-lin Liao, Jiwei Zhang +1
Due to the intrinsically initial singularity of solution and the discrete convolution form in numerical Caputo derivatives, the traditional -norm analysis (corresponding to th…
Unconditional convergence of a fast two-level linearized algorithm for semilinear subdiffusion equations
Hong-lin Liao, Yonggui Yan, Jiwei Zhang
A fast two-level linearized scheme with unequal time-steps is constructed and analyzed for an initial-boundary-value problem of semilinear subdiffusion equations. The two-level fas…
A discrete Grönwall inequality with application to numerical schemes for subdiffusion problems
Hong-lin Liao, William McLean, Jiwei Zhang
We consider a class of numerical approximations to the Caputo fractional derivative. Our assumptions permit the use of nonuniform time steps, such as is appropriate for accurately…
A second-order scheme with nonuniform time steps for a linear reaction-sudiffusion problem
Hong-lin Liao, William McLean, Jiwei Zhang
Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approxi…
Analysis of -Galerkin FEMs for time-fractional nonlinear parabolic problems
Dongfang Li, Hong-lin Liao, Weiwei Sun +2
This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of -Galerkin finite element methods. The analysis of methods fo…