92 citations · 322 across the 19 of their papers we have counts for
7 papers · 1 filter
A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system
Chen Liu, Beatrice Riviere, Jie Shen +1
For time-dependent PDEs, the numerical schemes can be rendered bound-preserving without losing conservation and accuracy, by a post processing procedure of solving a constrained mi…
An efficient and robust SAV based algorithm for discrete gradient systems arising from optimizations
Xinyu Liu, Jie Shen, Xiaongxiong Zhang
We propose in this paper a new minimization algorithm based on a slightly modified version of the scalar auxiliary variable (SAV) approach coupled with a relaxation step and an ada…
Eigenvalue Analysis and Applications of the Legendre Dual-Petrov-Galerkin Methods for Initial Value Problems
Desong Kong, Jie Shen, Li-Lian Wang +1
In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulted from the Legendre dual-Petrov-Galerkin (LDPG) method for the th-ord…
Energy Stability and Convergence of SAV Block-centered Finite Difference Method for Gradient Flows
Xiaoli Li, Jie Shen, Hongxing Rui
We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson schem…
Laguerre Functions and Their Applications to Tempered Fractional Differential Equaitons on Infinite Intervals
Sheng Chen, Jie Shen, Lilian Wang
Tempered fractional derivatives originated from the tempered fractional diffusion equations (TFDEs) modeled on the whole space R (see [23]). For numerically solving TFDEs, two kind…
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…
Generalized Jacobi Functions and Their Applications to Fractional Differential Equations
Sheng Chen, Jie Shen, Li-Lian Wang
In this paper, we consider spectral approximation of fractional differential equations (FDEs). A main ingredient of our approach is to define a new class of generalized Jacobi func…