7 papers
An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation
Kelong Cheng, Wenqiang Feng, Cheng Wang +1
In this paper we propose and analyze an energy stable numerical scheme for the Cahn-Hilliard equation, with second order accuracy in time and the fourth order finite difference app…
An Efficient Finite Difference Scheme for the 2D Sine-Gordon Equation
Xiaorong Kang, Wenqiang Feng, Kelong Cheng +1
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model the…
A Second-Order Energy Stable Backward Differentiation Formula Method for the Epitaxial Thin Film Equation with Slope Selection
Wenqiang Feng, Cheng Wang, Steven M. Wise +1
In this paper, we study a novel second-order energy stable Backward Differentiation Formula (BDF) finite difference scheme for the epitaxial thin film equation with slope selection…
Convergence Analysis and Numerical Implementation of a Second Order Numerical Scheme for the Three-Dimensional Phase Field Crystal Equation
Lixiu Dong, Wenqiang Feng, Cheng Wang +2
In this paper we analyze and implement a second-order-in-time numerical scheme for the three-dimensional phase field crystal (PFC) equation. The numerical scheme was proposed in [4…
A Second Order Energy Stable Scheme for the Cahn-Hilliard-Hele-Shaw Equations
Wenbin Chen, Wenqiang Feng, Yuan Liu +2
We present a second-order-in-time finite difference scheme for the Cahn-Hilliard-Hele-Shaw equations. This numerical method is uniquely solvable and unconditionally energy stable.…
An Energy Stable Finite-Difference Scheme for Functionalized Cahn-Hilliard Equation and its Convergence Analysis
Wenqiang Feng, Zhen Guan, John Lowengrub +2
We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with th…