209 citations · 396 across the 13 of their papers we have counts for
13 papers
Adaptive time-stepping and maximum-principle preserving Lagrangian schemes for gradient flows
Qianqian Liu, Wenbin Chen, Jie Shen +1
We develop in this paper an adaptive time-stepping approach for gradient flows with distinct treatments for conservative and non-conservative dynamics. For the non-conservative gra…
A new flow dynamic approach for Wasserstein gradient flows
Qing Cheng, Qianqian Liu, Wenbin Chen +1
We develop in this paper a new regularized flow dynamic approach to construct efficient numerical schemes for Wasserstein gradient flows in Lagrangian coordinates. Instead of appro…
Unique solvability and error analysis of the Lagrange multiplier approach for gradient flows
Qing Cheng, Jie Shen, Cheng Wang
The unique solvability and error analysis of the original Lagrange multiplier approach proposed in [8] for gradient flows is studied in this paper. We identify a necessary and suff…
A decoupled structure preserving scheme for the Poisson-Nernst-Planck Navier-Stokes equations and its error analysis
Ziyao Yu, Qing Cheng, Jie Shen +1
We consider in this paper a numerical approximation of Poisson-Nernst-Planck-Navier- Stokes (PNP-NS) system. We construct a decoupled semi-discrete and fully discrete scheme that e…
Length preserving numerical schemes for Landau-Lifshitz equation based on Lagrange multiplier approaches
Qing Cheng, Jie Shen
We develop in this paper two classes of length preserving schemes for the Landau-Lifshitz equation based on two different Lagrange multiplier approaches. In the first approach, the…
A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving
Qing Cheng, Jie Shen
In the second part of this series, we use the Lagrange multiplier approach proposed in the first part \cite{CheS21} to construct efficient and accurate bound and/or mass preserving…
A new Lagrange multiplier approach for constructing structure preserving schemes, I. positivity preserving
Qing Cheng, Jie Shen
We propose a new Lagrange multiplier approach to construct positivity preserving schemes for parabolic type equations. The new approach introduces a space-time Lagrange multiplier…
Modeling and simulation of nuclear architecture reorganization process using a phase field approach
Qing Cheng, Pourya Delafrouz, Jie Liang +2
We develop a special phase field/diffusive interface method to model the nuclear architecture reorganization process. In particular, we use a Lagrange multiplier approach in the ph…
The generalized scalar auxiliary variable approach (G-SAV) for gradient flows
Qing Cheng
We establish a general framework for developing, efficient energy stable numerical schemes for gradient flows and develop three classes of generalized scalar auxiliary variable app…
Global constraints preserving SAV schemes for gradient flows
Qing Cheng, Jie Shen
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with…
A new Lagrange Multiplier approach for gradient flows
Qing Cheng, Chun Liu, Jie Shen
We propose a new Lagrange Multiplier approach to design unconditional energy stable schemes for gradient flows. The new approach leads to unconditionally energy stable schemes that…
A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates, I. One-dimensional case
Q. Cheng, Chun liu, J. Shen
We develop a new Lagrangian approach --- flow dynamic approach to effectively capture the interface in the Allen-Cahn type equations. The underlying principle of this approach is t…
Efficient and accurate numerical schemes for a hydrodynamically coupled phase field diblock copolymer model
Qing Cheng, Xiaofeng Yang, Jie Shen
In this paper, we consider numerical approximations of a hydrodynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a grad…