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Author ID: shen.jie Recent zbMATH articles by "Shen, Jie"
Published as: Shen, Jie; Shen, J.
External Links: MGP
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Co-Authors

28 single-authored
23 Wang, Lilian
21 Yang, Xiaofeng
17 Liu, Chun
12 Cheng, Qing
10 Guo, Ben-Yu
10 Li, Xiaoli
8 Chen, Sheng
8 López, Juan Manuel
8 Sheng, Changtao
8 Xu, Chuanju
8 Xu, Jie
8 Yu, Haijun
7 Chen, Feng
7 Feng, James J.
7 Guermond, Jean-Luc
7 Huang, Fukeng
6 Marques, Francisco
6 Yue, Pengtao
5 An, Jing
5 Mao, Zhiping
5 Wang, Qi
5 Wang, Shouhong
5 Wang, Yingwei
5 Zhang, Xiangxiong
4 Bao, Weizhu
4 Chen, Lizhen
4 Gu, Yiqi
4 Ma, Lina
4 Nicholls, David P.
4 Tang, Tao
4 Temam, Roger Meyer
4 Wang, Zhongqing
4 Yang, Jiang
4 Zhuang, Qingqu
3 Cai, Yongyong
3 Dong, Suchuan
3 Forest, Mark Gregory
3 He, Ying
3 Li, Huiyuan
3 Wise, Steven M.
3 Wu, Ke
3 Zhang, Yanrong
2 Alici, Haydar
2 Azaïez, Mejdi
2 Cao, Duo
2 Chen, Hongtao
2 Chen, Wenbin
2 Chen, Ying
2 Choi, Heejun
2 Fang, Qirong
2 Guo, Zhichang
2 Hu, Jingwei
2 Hu, Lina
2 Huang, Can
2 Kwan, Yuen-Yick
2 Li, Peijun
2 Li, Ping
2 Liu, Qianqian
2 Liu, Xinyu
2 Liu, Zhengguang
2 Lu, Zhiming
2 Luo, Lishi
2 Mao, Jingjing
2 Michaux, Bertrand
2 Minev, Peter Dimitrov
2 Park, Jinhae
2 Pyo, Jae-Hong
2 Rakotoson, Jean-Michel
2 Sengul, Mustafa Taylan
2 Shen, Yi
2 Sun, Jiebao
2 Wang, Cheng
2 Wang, Langdi
2 Wang, Ruodu
2 Wang, Xiaoming
2 Wu, Jiahong
2 Xia, Jianlin
2 Xiu, Dongbin
2 Xu, Chenglong
2 Yang, Zhiguo
2 Yao, Wenjuan
2 Yuan, Juanming
2 Zhang, Zhimin
2 Zhao, Jia
2 Zheng, Nan
1 Antoine, Xavier
1 Bai, Xiangyu
1 Brahim, M. Mint
1 Brauner, Claude-Michel
1 Cai, Jiaxiang
1 Chandy, Abhilash J.
1 Chen, Falai
1 Chen, Jia
1 Chen, Zhi
1 Cheng, Ting
1 Cheng, Yongping
1 Colbert-Kelly, Sean
1 Cui, Zhenlu
1 Dai, C. M.
1 Delafrouz, Pourya
...and 110 more Co-Authors
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Serials

42 Journal of Computational Physics
29 SIAM Journal on Numerical Analysis
25 Journal of Scientific Computing
23 SIAM Journal on Scientific Computing
11 Mathematics of Computation
10 Applied Numerical Mathematics
9 Communications in Computational Physics
7 Computer Methods in Applied Mechanics and Engineering
7 Numerische Mathematik
6 Journal of Fluid Mechanics
5 Journal of Computational and Applied Mathematics
5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
5 Advances in Computational Mathematics
5 Discrete and Continuous Dynamical Systems
5 Discrete and Continuous Dynamical Systems. Series B
5 Communications in Mathematical Sciences
5 Numerical Mathematics: Theory, Methods and Applications
4 International Journal of Numerical Analysis and Modeling
4 East Asian Journal on Applied Mathematics
3 Mathematical Methods in the Applied Sciences
3 Physica D
3 Mathematical Problems in Engineering
3 Journal of Mathematical Study
3 Science China. Mathematics
2 IMA Journal of Numerical Analysis
2 International Journal for Numerical Methods in Fluids
2 Chinese Annals of Mathematics. Series B
2 Journal of Computational Mathematics
2 RAIRO. Modélisation Mathématique et Analyse Numérique
2 Applied Mathematics Letters
2 Machine Learning
2 Journal of Non-Newtonian Fluid Mechanics
2 Physics of Fluids
2 Journal of Liaoning Normal University. Natural Science Edition
2 Mathematical Biosciences and Engineering
2 Scientia Sinica. Mathematica
1 Applicable Analysis
1 Computers and Fluids
1 Computers & Mathematics with Applications
1 Computer Physics Communications
1 International Journal of Theoretical Physics
1 Wave Motion
1 Fluid Dynamics Research
1 Indiana University Mathematics Journal
1 Information Sciences
1 International Journal for Numerical Methods in Engineering
1 Numerical Functional Analysis and Optimization
1 Acta Applicandae Mathematicae
1 Journal of Statistical Computation and Simulation
1 SIAM Journal on Applied Mathematics
1 SIAM Review
1 Stochastic Processes and their Applications
1 Matemática Aplicada e Computacional
1 Advances in Differential Equations
1 Finance and Stochastics
1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
1 IEEE Transactions on Image Processing
1 Foundations of Computational Mathematics
1 Journal of Machine Learning Research (JMLR)
1 Multiscale Modeling & Simulation
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 Springer Series in Computational Mathematics
1 Computational & Mathematical Methods in Medicine
1 Kinetic and Related Models
1 Mathematics Monograph Series
1 Communications on Applied Mathematics and Computation
1 Journal of Computational Physics: X

Publications by Year

Citations contained in zbMATH Open

251 Publications have been cited 11,088 times in 5,024 Documents Cited by Year
Spectral methods. Algorithms, analysis and applications. Zbl 1227.65117
Shen, Jie; Tang, Tao; Wang, Li-Lian
2011
An overview of projection methods for incompressible flows. Zbl 1122.76072
Guermond, J. L.; Minev, P.; Shen, Jie
552
2006
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Zbl 1201.65184
Shen, Jie; Yang, Xiaofeng
511
2010
The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181
Shen, Jie; Xu, Jie; Yang, Jiang
479
2018
Efficient spectral-Galerkin method. I: Direct solvers of second- and fourth-order equations using Legendre polynomials. Zbl 0811.65097
Shen, Jie
322
1994
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Zbl 1092.76069
Liu, Chun; Shen, Jie
307
2003
A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080
Shen, Jie; Xu, Jie; Yang, Jiang
291
2019
A diffuse-interface method for simulating two-phase flows of complex fluids. Zbl 1130.76437
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
276
2004
Spectral and high-order methods with applications. Zbl 1234.65005
Shen, Jie; Tang, Tao
273
2006
Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: Application to thin film epitaxy. Zbl 1247.65088
Shen, Jie; Wang, Cheng; Wang, Xiaoming; Wise, Steven M.
258
2012
A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities. Zbl 1410.76464
Shen, Jie; Yang, Xiaofeng
194
2010
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047
Shen, Jie; Xu, Jie
178
2018
Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066
Chen, Sheng; Shen, Jie; Wang, Li-Lian
166
2016
Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178
Shen, Jie; Yang, Xiaofeng
166
2015
On error estimates of projection methods for Navier-Stokes equations: First-order schemes. Zbl 0741.76051
Shen, Jie
160
1992
Applications of semi-implicit Fourier-spectral method to phase field equations. Zbl 1017.65533
Chen, L. Q.; Shen, Jie
149
1998
Numerical approximations for a three-component Cahn-Hilliard phase-field model based on the invariant energy quadratization method. Zbl 1393.80003
Yang, Xiaofeng; Zhao, Jia; Wang, Qi; Shen, Jie
145
2017
On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes. Zbl 0855.76049
Shen, Jie
131
1996
On the error estimates for the rotational pressure-correction projection methods. Zbl 1093.76050
Guermond, J. L.; Shen, Jie
131
2004
Velocity-correction projection methods for incompressible flows. Zbl 1130.76395
Guermond, J. L.; Shen, Jie
125
2003
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. Zbl 1158.76319
Yang, Xiaofeng; Feng, James J.; Liu, Chun; Shen, Jie
122
2006
Long time stability and convergence for fully discrete nonlinear Galerkin methods. Zbl 0684.65095
Shen, Jie
114
1990
Efficient spectral-Galerkin method. II: Direct solvers of second- and fourth-order equations using Chebyshev polynomials. Zbl 0840.65113
Shen, Jie
112
1995
Stable and efficient spectral methods in unbounded domains using Laguerre functions. Zbl 0979.65105
Shen, Jie
102
2000
On error estimates of the penalty method for unsteady Navier-Stokes equations. Zbl 0822.35008
Shen, Jie
99
1995
On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059
Shen, Jie; Tang, Tao; Yang, Jiang
97
2016
Optimal spectral-Galerkin methods using generalized Jacobi polynomials. Zbl 1102.76047
Guo, Benyu; Shen, Jie; Wang, Li-Lian
92
2006
Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Zbl 1400.65049
Shen, Jie; Yang, Xiaofeng
87
2010
Some recent advances on spectral methods for unbounded domains. Zbl 1364.65265
Shen, Jie; Wang, Li-Lian
85
2009
A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. Zbl 1277.76118
Dong, S.; Shen, J.
84
2012
A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. Zbl 1084.35083
Bao, Weizhu; Shen, Jie
83
2005
A new class of truly consistent splitting schemes for incompressible flows. Zbl 1032.76529
Guermond, J. L.; Shen, Jie
80
2003
Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184
Shen, Jie; Yang, Xiaofeng; Yu, Haijun
80
2015
Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057
Shen, Jie; Yang, Xiaofeng
80
2014
Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Zbl 0969.65094
Guo, Ben-Yu; Shen, Jie
79
2000
A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KdV equation. Zbl 1053.65085
Shen, Jie
78
2003
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229
Chen, Ying; Shen, Jie
76
2016
Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations. Zbl 1382.65222
Mao, Zhiping; Chen, Sheng; Shen, Jie
73
2016
Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165
Li, Xiaoli; Shen, Jie; Rui, Hongxing
72
2019
Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. Zbl 1326.76064
Liu, Chun; Shen, Jie; Yang, Xiaofeng
72
2015
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045
Cheng, Qing; Shen, Jie
71
2018
Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1109.76037
Pyo, Jae-Hong; Shen, Jie
66
2007
Hopf bifurcation of the unsteady regularized driven cavity flow. Zbl 0725.76059
Shen, Jie
64
1991
A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids. Zbl 1349.76019
Zhao, Jia; Yang, Xiaofeng; Shen, Jie; Wang, Qi
62
2016
Efficient spectral-Galerkin methods. III: Polar and cylindrical geometries. Zbl 0890.65117
Shen, Jie
61
1997
A rational approximation and its applications to differential equations on the half line. Zbl 0984.65104
Guo, Benyu; Shen, Jie; Wang, Zhongqing
60
2000
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
60
2020
Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Zbl 1118.65111
Shen, Jie; Wang, Li-Lian
59
2007
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395
Mao, Zhiping; Shen, Jie
59
2016
Generalized Jacobi polynomials/functions and their applications. Zbl 1171.33006
Guo, Ben-Yu; Shen, Jie; Wang, Li-Lian
59
2009
Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach. Zbl 1444.76020
Cheng, Qing; Shen, Jie; Yang, Xiaofeng
54
2019
An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161
Collins, Craig; Shen, Jie; Wise, Steven M.
54
2013
Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions. Zbl 1083.76044
Guermond, J. L.; Minev, P.; Shen, J.
52
2005
An efficient moving mesh spectral method for the phase-field model of two-phase flows. Zbl 1159.76032
Shen, Jie; Yang, Xiaofeng
52
2009
A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210
Huang, Fukeng; Shen, Jie; Yang, Zhiguo
51
2020
On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0782.76025
Shen, Jie
51
1992
A generalized-Laguerre-Fourier-Hermite pseudospectral method for computing the dynamics of rotating Bose-Einstein condensates. Zbl 1205.82096
Bao, Weizhu; Li, Hailiang; Shen, Jie
51
2009
Spectral and pseudospectral approximations using Hermite functions: Application to the Dirac equation. Zbl 1032.33004
Guo, Ben-yu; Shen, Jie; Xu, Cheng-long
50
2003
Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval. Zbl 1001.65129
Guo, Benyu; Shen, Jie; Wang, Zhongqing
50
2002
Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems. Zbl 1388.65117
Chen, Feng; Shen, Jie
48
2013
The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems. Zbl 1484.65196
Shen, Jie; Yang, Xiaofeng
48
2020
Efficient stochastic Galerkin methods for random diffusion equations. Zbl 1161.65008
Xiu, Dongbin; Shen, Jie
47
2009
Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. Zbl 1380.65203
Cheng, Qing; Yang, Xiaofeng; Shen, Jie
44
2017
Efficient spectral sparse grid methods and applications to high-dimensional elliptic problems. Zbl 1233.65094
Shen, Jie; Yu, Haijun
43
2010
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437
Cai, Jiaxiang; Shen, Jie
41
2020
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
41
2005
Pressure boundary condition for the time-dependent incompressible Navier-Stokes equations. Zbl 1155.76322
Sani, R. L.; Shen, J.; Pironneau, O.; Gresho, P. M.
39
2006
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294
Li, Xiaoli; Shen, Jie
39
2020
On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line. Zbl 0992.65111
Guo, Ben-Yu; Shen, Jie
38
2001
Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167
Li, Xiaoli; Shen, Jie
38
2020
Remarks on the pressure error estimates for the projection methods. Zbl 0802.76060
Shen, Jie
37
1994
A spectral-element method for transmission eigenvalue problems. Zbl 1292.65119
An, Jing; Shen, Jie
37
2013
Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075
Mao, Zhiping; Shen, Jie
37
2017
An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. I: Axisymmetric cases. Zbl 0908.76068
Lopez, J. M.; Shen, Jie
36
1998
An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. Zbl 1181.76019
Feng, James J.; Liu, Chun; Shen, Jie; Yue, Pengtao
36
2005
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078
Liu, Fei; Shen, Jie
36
2015
Mass and volume conservation in phase field models for binary fluids. Zbl 1373.76317
Shen, Jie; Yang, Xiaofeng; Wang, Qi
35
2013
Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422
Liu, Chun; Shen, Jie; Yang, Xiaofeng
33
2007
Spectral approximation of the Helmholtz equation with high wave numbers. Zbl 1091.65119
Shen, Jie; Wang, Li-Lian
32
2005
On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0739.76017
Shen, Jie
32
1992
Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
31
2005
On numerical approximations of forward-backward stochastic differential equations. Zbl 1177.60064
Ma, Jin; Shen, Jie; Zhao, Yanhong
31
2008
Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains. Zbl 1154.65082
Shen, Jie; Wang, Li-Lian
31
2007
Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein condensates. Zbl 1452.65116
Zhuang, Qingqu; Shen, Jie
30
2019
Fast Fourier-like mapped Chebyshev spectral-Galerkin methods for PDEs with integral fractional Laplacian in unbounded domains. Zbl 1450.65154
Sheng, Changtao; Shen, Jie; Tang, Tao; Wang, Li-Lian; Yuan, Huifang
28
2020
A triangular spectral element method using fully tensorial rational basis functions. Zbl 1197.65187
Shen, Jie; Wang, Li-Lian; Li, Huiyuan
28
2009
Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. Zbl 1215.65179
Shen, Jie; Wang, Li-Lian
27
2010
Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. Zbl 1286.65112
Yang, Xiaofeng; Forest, M. Gregory; Li, Huiyuan; Liu, Chun; Shen, Jie; Wang, Qi; Chen, Falai
27
2013
Generalized Laguerre approximation and its applications to exterior problems. Zbl 1073.65130
Guo, Benyu; Shen, Jie; Xu, Chenglong
26
2005
A stable high-order method for two-dimensional bounded-obstacle scattering. Zbl 1130.78007
Nicholls, David P.; Shen, Jie
26
2006
Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Zbl 1382.35184
Cai, Yongyong; Choi, Heejun; Shen, Jie
26
2017
New SAV-pressure correction methods for the Navier-Stokes equations: stability and error Analysis. Zbl 1479.35625
Li, Xiaoli; Shen, Jie; Liu, Zhengguang
26
2022
Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305
Mao, Zhiping; Shen, Jie
25
2018
Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. Zbl 1416.65482
Shen, Jie; Wang, Yingwei
25
2016
Global constraints preserving scalar auxiliary variable schemes for gradient flows. Zbl 1456.65087
Cheng, Qing; Shen, Jie
24
2020
Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. Zbl 1440.65192
Chen, Hongtao; Mao, Jingjing; Shen, Jie
24
2020
Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. Zbl 1390.35225
Cai, Yongyong; Shen, Jie
24
2018
Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014
Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven
24
2018
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. Zbl 1123.76049
Fang, Qirong; Nicholls, David P.; Shen, Jie
24
2007
An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. II: Three-dimensional cases. Zbl 1130.76392
Lopez, J. M.; Marques, F.; Shen, Jie
23
2002
A Ginzburg-Landau-\({H}^{-1}\) model and its SAV algorithm for image inpainting. Zbl 1522.65164
Bai, Xiangyu; Sun, Jiebao; Shen, Jie; Yao, Wenjuan; Guo, Zhichang
2
2023
A fictitious domain spectral method for solving the Helmholtz equation in exterior domains. Zbl 1529.65135
Gu, Yiqi; Shen, Jie
1
2023
Log orthogonal functions in semi-infinite intervals: approximation results and applications. Zbl 1512.65278
Chen, Sheng; Shen, Jie
1
2023
A variable time-step IMEX-BDF2 SAV scheme and its sharp error estimate for the Navier-Stokes equations. Zbl 1529.65099
Di, Yana; Ma, Yuheng; Shen, Jie; Zhang, Jiwei
1
2023
New SAV-pressure correction methods for the Navier-Stokes equations: stability and error Analysis. Zbl 1479.35625
Li, Xiaoli; Shen, Jie; Liu, Zhengguang
26
2022
A new class of implicit-explicit BDF\(k\) SAV schemes for general dissipative systems and their error analysis. Zbl 1507.65152
Huang, Fukeng; Shen, Jie
20
2022
A generalized SAV approach with relaxation for dissipative systems. Zbl 07540356
Zhang, Yanrong; Shen, Jie
20
2022
A new Lagrange multiplier approach for constructing structure preserving schemes. I: Positivity preserving. Zbl 1507.65195
Cheng, Qing; Shen, Jie
15
2022
A new class of higher-order decoupled schemes for the incompressible Navier-Stokes equations and applications to rotating dynamics. Zbl 07527723
Wu, Ke; Huang, Fukeng; Shen, Jie
10
2022
Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations. Zbl 1492.65269
Li, Xiaoli; Wang, Weilong; Shen, Jie
10
2022
On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of two-phase incompressible flows. Zbl 07524187
Li, Xiaoli; Shen, Jie
9
2022
A new Lagrange multiplier approach for constructing structure preserving schemes. II: Bound preserving. Zbl 1491.65110
Cheng, Qing; Shen, Jie
9
2022
Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system. Zbl 1485.65102
Chen, Wenbin; Liu, Qianqian; Shen, Jie
7
2022
Discrete maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation. Zbl 1489.65124
Shen, Jie; Zhang, Xiangxiong
7
2022
Log orthogonal functions: approximation properties and applications. Zbl 1481.65037
Chen, Sheng; Shen, Jie
6
2022
Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation. Zbl 07595981
Li, Xiaoli; Shen, Jie
5
2022
Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations. Zbl 07525157
Huang, Fukeng; Shen, Jie; Wu, Ke
4
2022
Modeling and simulation of cell nuclear architecture reorganization process. Zbl 07524801
Cheng, Qing; Delafrouz, Pourya; Liang, Jie; Liu, Chun; Shen, Jie
2
2022
A fast Petrov-Galerkin spectral method for the multidimensional Boltzmann equation using mapped Chebyshev functions. Zbl 1490.35247
Hu, Jingwei; Huang, Xiaodong; Shen, Jie; Yang, Haizhao
2
2022
Boundary-confined waves in a librating cube. Zbl 07628418
Lopez, Juan M.; Shen, Jie; Welfert, Bruno D.; Wu, Ke
1
2022
Scalar auxiliary variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 07505911
Antoine, Xavier; Shen, Jie; Tang, Qinglin
22
2021
Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations. Zbl 1491.65086
Shen, Jie; Xu, Jie
19
2021
Generalized SAV approaches for gradient systems. Zbl 1475.65066
Cheng, Qing; Liu, Chun; Shen, Jie
14
2021
Bound/positivity preserving and energy stable scalar auxiliary variable schemes for dissipative systems: applications to Keller-Segel and Poisson-Nernst-Planck equations. Zbl 1512.65229
Huang, Fukeng; Shen, Jie
13
2021
A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations. Zbl 07508502
Li, Maojun; Cheng, Yongping; Shen, Jie; Zhang, Xiangxiong
12
2021
Stability and error analysis of a class of high-order IMEX schemes for Navier-Stokes equations with periodic boundary conditions. Zbl 1496.65180
Huang, Fukeng; Shen, Jie
11
2021
Efficient structure preserving schemes for the Klein-Gordon-Schrödinger equations. Zbl 1477.35198
Zhang, Yanrong; Shen, Jie
9
2021
An efficient spectral method for elliptic PDEs in complex domains with circular embedding. Zbl 1468.65211
Gu, Yiqi; Shen, Jie
5
2021
Computing interface with quasiperiodicity. Zbl 07508468
Cao, Duo; Shen, Jie; Xu, Jie
5
2021
Efficient and accurate SAV schemes for the generalized Zakharov systems. Zbl 1465.35362
Shen, Jie; Zheng, Nan
3
2021
Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis. Zbl 1491.65111
Deng, Beichuan; Shen, Jie; Zhuang, Qingqu
2
2021
Efficient spectral methods for PDEs with spectral fractional Laplacian. Zbl 1476.65320
Sheng, Changtao; Cao, Duo; Shen, Jie
1
2021
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
60
2020
A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210
Huang, Fukeng; Shen, Jie; Yang, Zhiguo
51
2020
The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems. Zbl 1484.65196
Shen, Jie; Yang, Xiaofeng
48
2020
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437
Cai, Jiaxiang; Shen, Jie
41
2020
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294
Li, Xiaoli; Shen, Jie
39
2020
Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167
Li, Xiaoli; Shen, Jie
38
2020
Fast Fourier-like mapped Chebyshev spectral-Galerkin methods for PDEs with integral fractional Laplacian in unbounded domains. Zbl 1450.65154
Sheng, Changtao; Shen, Jie; Tang, Tao; Wang, Li-Lian; Yuan, Huifang
28
2020
Global constraints preserving scalar auxiliary variable schemes for gradient flows. Zbl 1456.65087
Cheng, Qing; Shen, Jie
24
2020
Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. Zbl 1440.65192
Chen, Hongtao; Mao, Jingjing; Shen, Jie
24
2020
On a SAV-MAC scheme for the Cahn-Hilliard-Navier-Stokes phase-field model and its error analysis for the corresponding Cahn-Hilliard-Stokes case. Zbl 1471.65106
Li, Xiaoli; Shen, Jie
23
2020
A spectrally accurate approximation to subdiffusion equations using the log orthogonal functions. Zbl 1434.65291
Chen, Sheng; Shen, Jie; Zhang, Zhimin; Zhou, Zhi
21
2020
Unconditionally bound preserving and energy dissipative schemes for a class of Keller-Segel equations. Zbl 1440.65101
Shen, Jie; Xu, Jie
18
2020
Error estimate of Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1427.76124
Chen, Hongtao; Mao, Jingjing; Shen, Jie
9
2020
An efficient and accurate numerical method for the spectral fractional Laplacian equation. Zbl 1433.65235
Chen, Sheng; Shen, Jie
9
2020
A total fractional-order variation model for image super-resolution and its SAV algorithm. Zbl 1439.65100
Yao, Wenjuan; Shen, Jie; Guo, Zhichang; Sun, Jiebao; Wu, Boying
5
2020
Bound preserving and energy dissipative schemes for porous medium equation. Zbl 1436.65101
Gu, Yiqi; Shen, Jie
5
2020
Accurate and efficient spectral methods for elliptic PDEs in complex domains. Zbl 1440.65160
Gu, Yiqi; Shen, Jie
4
2020
A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions. Zbl 1446.65128
Hu, Jingwei; Shen, Jie; Wang, Yingwei
3
2020
Stability and error analysis of operator splitting methods for American options under the Black-Scholes model. Zbl 1433.91173
Chen, Feng; Shen, Jie
3
2020
A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates. I: One-dimensional case. Zbl 07507218
Cheng, Qing; Liu, Chun; Shen, Jie
3
2020
A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080
Shen, Jie; Xu, Jie; Yang, Jiang
291
2019
Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165
Li, Xiaoli; Shen, Jie; Rui, Hongxing
72
2019
Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach. Zbl 1444.76020
Cheng, Qing; Shen, Jie; Yang, Xiaofeng
54
2019
Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein condensates. Zbl 1452.65116
Zhuang, Qingqu; Shen, Jie
30
2019
An efficient space-time method for time fractional diffusion equation. Zbl 1466.65214
Shen, Jie; Sheng, Chang-Tao
12
2019
Stability and convergence analysis of rotational velocity correction methods for the Navier-Stokes equations. Zbl 1435.65119
Chen, Feng; Shen, Jie
10
2019
Distributional compatibility for change of measures. Zbl 1420.60027
Shen, Jie; Shen, Yi; Wang, Bin; Wang, Ruodu
5
2019
Efficient and accurate structure preserving schemes for complex nonlinear systems. Zbl 1446.65213
Shen, Jie
5
2019
Fast structured Jacobi-Jacobi transforms. Zbl 07040627
Shen, Jie; Wang, Yingwei; Xia, Jianlin
4
2019
Fundamental gaps of the fractional Schrödinger operator. Zbl 1429.35195
Bao, Weizhu; Ruan, Xinran; Shen, Jie; Sheng, Changtao
3
2019
The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181
Shen, Jie; Xu, Jie; Yang, Jiang
479
2018
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047
Shen, Jie; Xu, Jie
178
2018
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045
Cheng, Qing; Shen, Jie
71
2018
Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305
Mao, Zhiping; Shen, Jie
25
2018
Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. Zbl 1390.35225
Cai, Yongyong; Shen, Jie
24
2018
Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014
Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven
24
2018
Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy. Zbl 1475.82027
Shen, Jie; Xu, Jie
17
2018
Laguerre functions and their applications to tempered fractional differential equations on infinite intervals. Zbl 1398.65314
Chen, Sheng; Shen, Jie; Wang, Li-Lian
14
2018
A tight bound of hard thresholding. Zbl 1473.62287
Shen, Jie; Li, Ping
12
2018
A space-time Petrov-Galerkin spectral method for time fractional diffusion equation. Zbl 1438.65308
Sheng, Changtao; Shen, Jie
11
2018
Enriched spectral methods and applications to problems with weakly singular solutions. Zbl 1406.65123
Chen, Sheng; Shen, Jie
11
2018
Highly efficient and accurate spectral approximation of the angular Mathieu equation for any parameter values \(q\). Zbl 1424.65119
Alici, Haydar; Shen, Jie
4
2018
Wavenumber explicit analysis for time-harmonic Maxwell equations in a spherical shell and spectral approximations. Zbl 1477.78001
Ma, Lina; Shen, Jie; Wang, Li-Lian; Yang, Zhiguo
4
2018
Preconditioning techniques in Chebyshev collocation method for elliptic equations. Zbl 1408.35025
Fang, Zhi-Wei; Shen, Jie; Sun, Hai-Wei
2
2018
The spectral-Galerkin approximation of nonlinear eigenvalue problems. Zbl 1394.65137
An, Jing; Shen, Jie; Zhang, Zhimin
2
2018
Approximations on \(\mathrm{SO}(3)\) by Wigner D-matrix and applications. Zbl 1398.65321
Shen, Jie; Xu, Jie; Zhang, Pingwen
1
2018
Numerical approximations for a three-component Cahn-Hilliard phase-field model based on the invariant energy quadratization method. Zbl 1393.80003
Yang, Xiaofeng; Zhao, Jia; Wang, Qi; Shen, Jie
145
2017
Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. Zbl 1380.65203
Cheng, Qing; Yang, Xiaofeng; Shen, Jie
44
2017
Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075
Mao, Zhiping; Shen, Jie
37
2017
Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Zbl 1382.35184
Cai, Yongyong; Choi, Heejun; Shen, Jie
26
2017
Unconditionally stable Gauge-Uzawa finite element schemes for incompressible natural convection problems with variable density. Zbl 1380.76132
Wu, Jilian; Shen, Jie; Feng, Xinlong
19
2017
A hybrid spectral element method for fractional two-point boundary value problems. Zbl 1413.65307
Sheng, Changtao; Shen, Jie
15
2017
A stable scheme and its convergence analysis for a 2D dynamic \(Q\)-tensor model of nematic liquid crystals. Zbl 1368.76048
Cai, Yongyong; Shen, Jie; Xu, Xiang
9
2017
The generation of symmetric and asymmetric lumps by a bottom topography. Zbl 1524.35539
Hu, Wencheng; Huang, Wenhua; Shen, Jie; Lu, Zhiming
2
2017
A nodal sparse grid spectral element method for multi-dimensional elliptic partial differential equations. Zbl 1429.65287
Rong, Zhijian; Shen, Jie; Yu, Haijun
2
2017
Numerical analysis and simulation for a generalized planar Ginzburg-Landau equation in a circular geometry. Zbl 1367.65142
Colbert-Kelly, Sean; McFadden, Geoffrey B.; Phillips, Daniel; Shen, Jie
2
2017
Online optimization for max-norm regularization. Zbl 1454.68132
Shen, Jie; Xu, Huan; Li, Ping
2
2017
Highly accurate pseudospectral approximations of the prolate spheroidal wave equation for any bandwidth parameter and zonal wavenumber. Zbl 1416.65224
Alıcı, H.; Shen, Jie
1
2017
Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066
Chen, Sheng; Shen, Jie; Wang, Li-Lian
166
2016
On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059
Shen, Jie; Tang, Tao; Yang, Jiang
97
2016
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229
Chen, Ying; Shen, Jie
76
2016
Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations. Zbl 1382.65222
Mao, Zhiping; Chen, Sheng; Shen, Jie
73
2016
A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids. Zbl 1349.76019
Zhao, Jia; Yang, Xiaofeng; Shen, Jie; Wang, Qi
62
2016
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395
Mao, Zhiping; Shen, Jie
59
2016
Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. Zbl 1416.65482
Shen, Jie; Wang, Yingwei
25
2016
Efficient splitting schemes for magneto-hydrodynamic equations. Zbl 1388.76224
Choi, Heejun; Shen, Jie
21
2016
Fast structured direct spectral methods for differential equations with variable coefficients. I. The one-dimensional case. Zbl 1330.65124
Shen, Jie; Wang, Yingwei; Xia, Jianlin
13
2016
A hybrid spectral element method for Volterra integral equations with weakly singular kernel. Zbl 1499.65770
Sheng, Changtao; Shen, Jie
3
2016
...and 151 more Documents
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Cited by 5,556 Authors

124 Shen, Jie
120 Yang, Xiaofeng
60 He, Yinnian
60 Kim, Junseok
59 Wang, Cheng
58 Guo, Ben-Yu
54 Feng, Xinlong
54 Wang, Lilian
53 Wang, Yushun
48 Wang, Qi
46 Chen, Yanping
46 Zhao, Jia
45 Wang, Zhongqing
42 Wise, Steven M.
42 Zhang, Zhimin
39 Dehghan Takht Fooladi, Mehdi
39 Mei, Liquan
37 Huang, Yunqing
36 Gong, Yuezheng
35 Zaky, Mahmoud A.
34 Li, Huiyuan
34 Liu, Chun
34 Xu, Chuanju
32 Doha, Eid H.
32 Karniadakis, George Em
32 Li, Yibao
32 Wang, Hong
30 Chen, Wenbin
30 Jiang, Xiaoyun
30 Zhang, Jun
29 Bao, Weizhu
29 Dong, Suchuan
29 Ju, Lili
29 Qiao, Zhonghua
29 Yang, Junxiang
27 Li, Xiaoli
27 Wang, Tianjun
26 Cai, Wenjun
26 Chen, Chuanjun
26 Sun, Shuyu
25 Du, Qiang
25 Hou, Yanren
25 Parand, Kourosh
25 Tang, Tao
24 Kou, Jisheng
24 Nicholls, David P.
24 Wang, Xiaoming
23 Bhrawy, Ali Hassan
23 Han, Daozhi
23 He, Xiaoming
23 Zheng, Xiangcheng
22 An, Jing
22 Guermond, Jean-Luc
22 Jiang, Chaolong
22 López, Juan Manuel
22 Song, Songhe
21 Lee, Hyun Geun
21 Liu, Fawang
21 Qian, Xu
21 Zhang, Luming
20 Cai, Yongyong
20 Hendy, Ahmed S.
20 Li, Jian
20 Lin, Ping
20 Liu, Wen-Jie
19 Chen, Lizhen
19 Guillén González, Francisco M.
19 Jia, Hongen
19 Li, Buyang
19 Lu, Shujuan
19 Ma, Heping
19 Miranville, Alain M.
19 Yang, Yidu
19 Yang, Yin
19 Zhang, Tong
18 Li, Dongfang
18 Mao, Zhiping
18 Su, Haiyan
18 Wu, Boying
18 Yang, Jiang
18 Zhang, Zhengru
17 Liu, Zhengguang
17 Yi, Lijun
17 Zhang, Hong
17 Zhou, Jianwei
16 Azaïez, Mejdi
16 Bi, Hai
16 Huang, Chengming
16 Li, Xiao
16 Marques, Francisco
16 Mokhtary, Payam
16 Wang, Quan
16 Wu, Hao
16 Zhang, Hui
15 Eslahchi, Mohammad Reza
15 Hong, Qi
15 Hou, Dianming
15 Lowengrub, John Samuel
15 Minev, Peter Dimitrov
15 Si, Zhiyong
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636 Journal of Computational Physics
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9 Comptes Rendus. Mathématique. Académie des Sciences, Paris
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8 Boundary Value Problems
7 ZAMP. Zeitschrift für angewandte Mathematik und Physik
7 Acta Mathematica Scientia. Series B. (English Edition)
7 Multiscale Modeling & Simulation
7 Acta Numerica
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