365 citations · 921 across the 25 of their papers we have counts for
25 papers
A high-order nodally bound-preserving and mass-conservative method for linear fourth-order elliptic problems and its applications to nonlinear parabolic equations
Jie Shen, Zuodong Wang
We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequali…
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 generalized SAV approach with relaxation for dissipative systems
Yanrong Zhang, Jie Shen
The scalar auxiliary variable (SAV) approach \cite{shen2018scalar} and its generalized version GSAV proposed in \cite{huang2020highly} are very popular methods to construct efficie…
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…
Strong convergence rates of a fully discrete scheme for nonlinear stochastic partial differential equations with non-globally Lipschitz coefficients driven by multiplicative noise
Can Huang, Jie Shen
We consider a fully discrete scheme for nonlinear stochastic partial differential equations with non-globally Lipschitz coefficients driven by multiplicative noise in a multi-dimen…
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…
A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions
Jingwei Hu, Xiaodong Huang, Jie Shen +1
Numerical approximation of the Boltzmann equation presents a challenging problem due to its high-dimensional, nonlinear, and nonlocal collision operator. Among the deterministic me…
Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation
Jie Shen, Xiangxiong Zhang
We consider solving a generalized Allen-Cahn equation coupled with a passive convection for a given incompressible velocity field. The numerical scheme consists of the first order…
Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations
Xiaoli Li, Weilong Wang, Jie Shen
We construct and analyze first- and second-order implicit-explicit (IMEX) schemes based on the scalar auxiliary variable (SAV) approach for the magneto-hydrodynamic equations. Thes…
Stability and error analysis of a class of high-order IMEX schemes for Navier-stokes equations with periodic boundary conditions
Fukeng Huang, Jie Shen
We construct high-order semi-discrete-in-time and fully discrete (with Fourier-Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary cond…
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…
Implicit-explicit BDF SAV schemes for general dissipative systems and their error analysis
Fukeng Huang, Jie Shen
We construct efficient implicit-explicit BDF scalar auxiliary variable (SAV) schemes for general dissipative systems. We show that these schemes are unconditionally stable, and…
On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows
Xiaoli Li, Jie Shen
We construct first- and second-order time discretization schemes for the Cahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary variables approach (MSAV) approac…
Unconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations
Jie Shen, Jie Xu
We develop a set of numerical schemes for the Poisson--Nernst--Planck equations. We prove that our schemes are mass conservative, uniquely solvable and keep positivity unconditiona…
Efficient Linear and Unconditionally Energy Stable Schemes for the Modified Phase Field Crystal Equation
Xiaoli Li, Jie Shen
In this paper, we construct efficient schemes based on the scalar auxiliary variable (SAV) block-centered finite difference method for the modified phase field crystal (MPFC) equat…
Log orthogonal functions: approximation properties and applications
Sheng Chen, Jie Shen
We present two new classes of orthogonal functions, log orthogonal functions (LOFs) and generalized log orthogonal functions (GLOFs), which are constructed by applying a map…
New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
Xiaoli Li, Jie Shen, Zhengguang Liu
We construct new first- and second-order pressure correction schemes using the scalar auxiliary variable (SAV) approach for the Navier-Stokes equations. These schemes are linear, d…
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…
An efficient numerical scheme for a 3D spherical dynamo equation
Ting cheng, Lina Ma, Jie Shen
We develop an efficient numerical scheme for the 3D mean-field spherical dynamo equation. The scheme is based on a semi-implicit discretization in time and a spectral method in spa…
Error analysis of the SAV-MAC scheme for the Navier-Stokes equations
Xiaoli Li, Jie Shen
An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell scheme (MAC) is constructed for the Navier-Stokes equations. A particular feature of…
Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains
Changtao Sheng, Jie Shen, Tao Tang +2
In this paper, we propose a fast spectral-Galerkin method for solving PDEs involving integral fractional Laplacian in , which is built upon two essential components:…
Fundamental Gaps of the Fractional Schrödinger Operator
Weizhu Bao, Xinran Ruan, Jie Shen +1
We study asymptotically and numerically the fundamental gap -- the difference between the first two smallest (and distinct) eigenvalues -- of the fractional Schrödinger operator (F…
Numerical Approximations for a three components Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method
Xiaofeng Yang, Jia Zhao, Qi Wang +1
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field mode…