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Author ID: shen.jie Recent zbMATH articles by "Shen, Jie"
Published as: Shen, Jie; Shen, J.
External Links: MGP
Documents Indexed: 265 Publications since 1988, including 2 Books
5 Contributions as Editor
Biographic References: 1 Publication
Co-Authors: 108 Co-Authors with 192 Joint Publications
4,313 Co-Co-Authors
all top 5

Co-Authors

27 single-authored
22 Wang, Lilian
21 Yang, Xiaofeng
17 Liu, Chun
10 Cheng, Qing
10 Guo, Ben-Yu
8 Sheng, Changtao
8 Xu, Chuanju
8 Xu, Jie
8 Yu, Haijun
7 Chen, Feng
7 Feng, James J.
7 Guermond, Jean-Luc
7 Li, Xiaoli
7 López, Juan Manuel
6 Huang, Fukeng
6 Marques, Francisco
6 Yue, Pengtao
5 An, Jing
5 Mao, Zhiping
5 Wang, Qi
5 Wang, Shouhong
5 Wang, Yingwei
4 Bao, Weizhu
4 Chen, Lizhen
4 Ma, Lina
4 Nicholls, David P.
4 Tang, Tao
4 Temam, Roger Meyer
4 Wang, Zhongqing
4 Zhuang, Qingqu
3 Cai, Yongyong
3 Forest, Mark Gregory
3 Gu, Yiqi
3 He, Ying
3 Li, Huiyuan
3 Wise, Steven M.
3 Yang, Jiang
2 Alici, Haydar
2 Azaïez, Mejdi
2 Cao, Duo
2 Chen, Hongtao
2 Choi, Heejun
2 Fang, Qirong
2 Hu, Jingwei
2 Hu, Lina
2 Kwan, Yuen-Yick
2 Li, Peijun
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 Wang, Cheng
2 Wang, Langdi
2 Wang, Ruodu
2 Wang, Xiaoming
2 Wu, Jiahong
2 Wu, Ke
2 Xia, Jianlin
2 Xiu, Dongbin
2 Xu, Chenglong
2 Yang, Zhiguo
2 Yuan, Juanming
2 Zhang, Xiangxiong
2 Zhang, Yanrong
2 Zhao, Jia
1 Antoine, Xavier
1 Brahim, M. Mint
1 Brauner, Claude-Michel
1 Cai, Jiaxiang
1 Chandy, Abhilash J.
1 Chen, Falai
1 Chen, Jia
1 Chen, Wenbin
1 Chen, Zhi
1 Cheng, Ting
1 Cheng, Yongping
1 Colbert-Kelly, Sean
1 Cui, Zhenlu
1 Dai, C. M.
1 Delafrouz, Pourya
1 Demkowicz, Leszek F.
1 Deng, Beichuan
1 Dijkstra, Henk A.
1 Du, Qiang
1 Fang, Yuqiang
1 Fang, Zhiwei
1 Feng, Xinlong
1 Fisher, Thomas J.
1 Frankel, Steven H.
1 Gallagher, Colin M.
1 Gebremariam, Tesfay
1 Goubet, Olivier
1 Gresho, Philip M.
1 Guo, Benqi
1 Guo, Zhichang
...and 72 more Co-Authors
all top 5

Serials

40 Journal of Computational Physics
27 SIAM Journal on Numerical Analysis
23 Journal of Scientific Computing
21 SIAM Journal on Scientific Computing
10 Mathematics of Computation
9 Applied Numerical Mathematics
9 Communications in Computational Physics
7 Computer Methods in Applied Mechanics and Engineering
7 Numerische Mathematik
5 Journal of Fluid Mechanics
5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
5 Advances in Computational Mathematics
5 Discrete and Continuous Dynamical Systems
5 Communications in Mathematical Sciences
5 Numerical Mathematics: Theory, Methods and Applications
4 Journal of Computational and Applied Mathematics
4 Discrete and Continuous Dynamical Systems. Series B
4 International Journal of Numerical Analysis and Modeling
3 Mathematical Methods in the Applied Sciences
3 Physica D
3 Mathematical Problems in Engineering
3 Journal of Mathematical Study
3 East Asian Journal on Applied 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 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 Physics Letters. A
1 Wave Motion
1 Fluid Dynamics Research
1 Indiana University Mathematics Journal
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 Mathematical Biosciences and Engineering
1 Springer Series in Computational Mathematics
1 Computational & Mathematical Methods in Medicine
1 Kinetic and Related Models
1 Science China. Mathematics
1 Mathematics Monograph Series
1 Communications on Applied Mathematics and Computation

Publications by Year

Citations contained in zbMATH Open

230 Publications have been cited 7,965 times in 3,625 Documents Cited by Year
An overview of projection methods for incompressible flows. Zbl 1122.76072
Guermond, J. L.; Minev, P.; Shen, Jie
421
2006
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Zbl 1201.65184
Shen, Jie; Yang, Xiaofeng
361
2010
Spectral methods. Algorithms, analysis and applications. Zbl 1227.65117
Shen, Jie; Tang, Tao; Wang, Li-Lian
355
2011
The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181
Shen, Jie; Xu, Jie; Yang, Jiang
284
2018
Efficient spectral-Galerkin method. I: Direct solvers of second- and fourth-order equations using Legendre polynomials. Zbl 0811.65097
Shen, Jie
283
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
234
2003
A diffuse-interface method for simulating two-phase flows of complex fluids. Zbl 1130.76437
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
230
2004
Spectral and high-order methods with applications. Zbl 1234.65005
Shen, Jie; Tang, Tao
209
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.
183
2012
A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080
Shen, Jie; Xu, Jie; Yang, Jiang
148
2019
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
143
2010
Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066
Chen, Sheng; Shen, Jie; Wang, Li-Lian
131
2016
On error estimates of projection methods for Navier-Stokes equations: First-order schemes. Zbl 0741.76051
Shen, Jie
125
1992
Applications of semi-implicit Fourier-spectral method to phase field equations. Zbl 1017.65533
Chen, L. Q.; Shen, Jie
120
1998
Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178
Shen, Jie; Yang, Xiaofeng
115
2015
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047
Shen, Jie; Xu, Jie
111
2018
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
110
2006
Efficient spectral-Galerkin method. II: Direct solvers of second- and fourth-order equations using Chebyshev polynomials. Zbl 0840.65113
Shen, Jie
108
1995
On the error estimates for the rotational pressure-correction projection methods. Zbl 1093.76050
Guermond, J. L.; Shen, Jie
103
2004
On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes. Zbl 0855.76049
Shen, Jie
99
1996
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
98
2017
Velocity-correction projection methods for incompressible flows. Zbl 1130.76395
Guermond, J. L.; Shen, Jie
97
2003
Stable and efficient spectral methods in unbounded domains using Laguerre functions. Zbl 0979.65105
Shen, Jie
94
2000
Long time stability and convergence for fully discrete nonlinear Galerkin methods. Zbl 0684.65095
Shen, Jie
93
1990
Optimal spectral-Galerkin methods using generalized Jacobi polynomials. Zbl 1102.76047
Guo, Benyu; Shen, Jie; Wang, Li-Lian
84
2006
On error estimates of the penalty method for unsteady Navier-Stokes equations. Zbl 0822.35008
Shen, Jie
82
1995
Some recent advances on spectral methods for unbounded domains. Zbl 1364.65265
Shen, Jie; Wang, Li-Lian
75
2009
Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Zbl 0969.65094
Guo, Ben-Yu; Shen, Jie
72
2000
Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Zbl 1400.65049
Shen, Jie; Yang, Xiaofeng
69
2010
A new class of truly consistent splitting schemes for incompressible flows. Zbl 1032.76529
Guermond, J. L.; Shen, Jie
68
2003
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.
68
2012
A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. Zbl 1084.35083
Bao, Weizhu; Shen, Jie
67
2005
A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KdV equation. Zbl 1053.65085
Shen, Jie
66
2003
Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184
Shen, Jie; Yang, Xiaofeng; Yu, Haijun
63
2015
On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059
Shen, Jie; Tang, Tao; Yang, Jiang
60
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
59
2016
Hopf bifurcation of the unsteady regularized driven cavity flow. Zbl 0725.76059
Shen, Jie
59
1991
Efficient spectral-Galerkin methods. III: Polar and cylindrical geometries. Zbl 0890.65117
Shen, Jie
54
1997
A rational approximation and its applications to differential equations on the half line. Zbl 0984.65104
Guo, Benyu; Shen, Jie; Wang, Zhongqing
52
2000
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395
Mao, Zhiping; Shen, Jie
50
2016
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
49
2015
Generalized Jacobi polynomials/functions and their applications. Zbl 1171.33006
Guo, Ben-Yu; Shen, Jie; Wang, Li-Lian
48
2009
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
47
2016
An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161
Collins, Craig; Shen, Jie; Wise, Steven M.
47
2013
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045
Cheng, Qing; Shen, Jie
47
2018
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229
Chen, Ying; Shen, Jie
46
2016
Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1109.76037
Pyo, Jae-Hong; Shen, Jie
46
2007
Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Zbl 1118.65111
Shen, Jie; Wang, Li-Lian
46
2007
Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057
Shen, Jie; Yang, Xiaofeng
45
2014
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.
42
2005
An efficient moving mesh spectral method for the phase-field model of two-phase flows. Zbl 1159.76032
Shen, Jie; Yang, Xiaofeng
42
2009
Spectral and pseudospectral approximations using Hermite functions: Application to the Dirac equation. Zbl 1032.33004
Guo, Ben-yu; Shen, Jie; Xu, Cheng-long
40
2003
Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems. Zbl 1388.65117
Chen, Feng; Shen, Jie
40
2013
Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval. Zbl 1001.65129
Guo, Benyu; Shen, Jie; Wang, Zhongqing
40
2002
Efficient spectral sparse grid methods and applications to high-dimensional elliptic problems. Zbl 1233.65094
Shen, Jie; Yu, Haijun
38
2010
Efficient stochastic Galerkin methods for random diffusion equations. Zbl 1161.65008
Xiu, Dongbin; Shen, Jie
37
2009
Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165
Li, Xiaoli; Shen, Jie; Rui, Hongxing
36
2019
On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0782.76025
Shen, Jie
36
1992
An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. I: Axisymmetric cases. Zbl 0908.76068
Lopez, J. M.; Shen, Jie
35
1998
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
35
2005
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
35
2019
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
34
2005
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
34
2009
Pressure boundary condition for the time-dependent incompressible Navier-Stokes equations. Zbl 1155.76322
Sani, R. L.; Shen, J.; Pironneau, O.; Gresho, P. M.
34
2006
Remarks on the pressure error estimates for the projection methods. Zbl 0802.76060
Shen, Jie
32
1994
Spectral approximation of the Helmholtz equation with high wave numbers. Zbl 1091.65119
Shen, Jie; Wang, Li-Lian
31
2005
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
30
2001
Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains. Zbl 1154.65082
Shen, Jie; Wang, Li-Lian
29
2007
Mass and volume conservation in phase field models for binary fluids. Zbl 1373.76317
Shen, Jie; Yang, Xiaofeng; Wang, Qi
29
2013
A spectral-element method for transmission eigenvalue problems. Zbl 1292.65119
An, Jing; Shen, Jie
29
2013
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
29
2020
Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. Zbl 1380.65203
Cheng, Qing; Yang, Xiaofeng; Shen, Jie
28
2017
Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
27
2005
On numerical approximations of forward-backward stochastic differential equations. Zbl 1177.60064
Ma, Jin; Shen, Jie; Zhao, Yanhong
26
2008
Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. Zbl 1215.65179
Shen, Jie; Wang, Li-Lian
26
2010
On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0739.76017
Shen, Jie
25
1992
A stable high-order method for two-dimensional bounded-obstacle scattering. Zbl 1130.78007
Nicholls, David P.; Shen, Jie
24
2006
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
24
2013
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078
Liu, Fei; Shen, Jie
23
2015
Generalized Laguerre approximation and its applications to exterior problems. Zbl 1073.65130
Guo, Benyu; Shen, Jie; Xu, Chenglong
23
2005
A triangular spectral element method using fully tensorial rational basis functions. Zbl 1197.65187
Shen, Jie; Wang, Li-Lian; Li, Huiyuan
23
2009
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. Zbl 1123.76049
Fang, Qirong; Nicholls, David P.; Shen, Jie
23
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
An efficient spectral method for acoustic scattering from rough surfaces. Zbl 1164.65303
Xiu, Dongbin; Shen, Jie
22
2007
Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422
Liu, Chun; Shen, Jie; Yang, Xiaofeng
22
2007
Mode interactions in an enclosed swirling flow: A double Hopf bifurcation between azimuthal wavenumbers 0 and 2. Zbl 1016.76029
Marques, F.; Lopez, J. M.; Shen, J.
22
2002
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437
Cai, Jiaxiang; Shen, Jie
21
2020
Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle. Zbl 1197.65176
Li, Huiyuan; Shen, Jie
20
2010
Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075
Mao, Zhiping; Shen, Jie
19
2017
Instability and mode interactions in a differentially driven rotating cylinder. Zbl 1042.76026
Lopez, J. M.; Hart, J. E.; Marques, F.; Kittelman, S.; Shen, J.
19
2002
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
19
2018
A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210
Huang, Fukeng; Shen, Jie; Yang, Zhiguo
19
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
18
2020
Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305
Mao, Zhiping; Shen, Jie
18
2018
Legendre and Chebyshev dual-Petrov-Galerkin methods for hyperbolic equations. Zbl 1173.65342
Shen, Jie; Wang, Li-Lian
18
2007
On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval. Zbl 1157.35093
Goubet, Olivier; Shen, Jie
17
2007
On liquid crystal flows with free-slip boundary conditions. Zbl 1014.76005
Liu, Chun; Shen, Jie
17
2001
An unconditionally stable rotational velocity-correction scheme for incompressible flows. Zbl 1425.76058
Dong, S.; Shen, J.
17
2010
Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. Zbl 1349.65721
Shen, Jie; Sheng, Changtao; Wang, Zhongqing
17
2015
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
17
2017
New SAV-pressure correction methods for the Navier-Stokes equations: stability and error Analysis. Zbl 1479.35625
Li, Xiaoli; Shen, Jie; Liu, Zhengguang
5
2022
A new Lagrange multiplier approach for constructing structure preserving schemes. I: Positivity preserving. Zbl 07487691
Cheng, Qing; Shen, Jie
2
2022
Log orthogonal functions: approximation properties and applications. Zbl 1481.65037
Chen, Sheng; Shen, Jie
1
2022
Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations. Zbl 07525157
Huang, Fukeng; Shen, Jie; Wu, Ke
1
2022
A new class of implicit-explicit BDF\(k\) SAV schemes for general dissipative systems and their error analysis. Zbl 07526020
Huang, Fukeng; Shen, Jie
1
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
1
2022
A generalized SAV approach with relaxation for dissipative systems. Zbl 07540356
Zhang, Yanrong; Shen, Jie
1
2022
Discrete maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation. Zbl 1489.65124
Shen, Jie; Zhang, Xiangxiong
1
2022
Generalized SAV approaches for gradient systems. Zbl 1475.65066
Cheng, Qing; Liu, Chun; Shen, Jie
6
2021
Bound/positivity preserving and energy stable scalar auxiliary variable schemes for dissipative systems: applications to Keller-Segel and Poisson-Nernst-Planck equations. Zbl 07364339
Huang, Fukeng; Shen, Jie
5
2021
Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations. Zbl 1491.65086
Shen, Jie; Xu, Jie
5
2021
Stability and error analysis of a class of high-order IMEX schemes for Navier-Stokes equations with periodic boundary conditions. Zbl 07453432
Huang, Fukeng; Shen, Jie
3
2021
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
2
2021
Efficient and accurate SAV schemes for the generalized Zakharov systems. Zbl 1465.35362
Shen, Jie; Zheng, Nan
1
2021
Computing interface with quasiperiodicity. Zbl 07508468
Cao, Duo; Shen, Jie; Xu, Jie
1
2021
A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations. Zbl 07508502
Li, Maojun; Cheng, Yongping; Shen, Jie; Zhang, Xiangxiong
1
2021
Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis. Zbl 1491.65111
Deng, Beichuan; Shen, Jie; Zhuang, Qingqu
1
2021
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
29
2020
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437
Cai, Jiaxiang; Shen, Jie
21
2020
A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210
Huang, Fukeng; Shen, Jie; Yang, Zhiguo
19
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
18
2020
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294
Li, Xiaoli; Shen, Jie
17
2020
Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167
Li, Xiaoli; Shen, Jie
17
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
13
2020
Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. Zbl 1440.65192
Chen, Hongtao; Mao, Jingjing; Shen, Jie
10
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
9
2020
A spectrally accurate approximation to subdiffusion equations using the log orthogonal functions. Zbl 1434.65291
Chen, Sheng; Shen, Jie; Zhang, Zhimin; Zhou, Zhi
9
2020
Global constraints preserving scalar auxiliary variable schemes for gradient flows. Zbl 1456.65087
Cheng, Qing; Shen, Jie
9
2020
Unconditionally bound preserving and energy dissipative schemes for a class of Keller-Segel equations. Zbl 1440.65101
Shen, Jie; Xu, Jie
6
2020
Bound preserving and energy dissipative schemes for porous medium equation. Zbl 1436.65101
Gu, Yiqi; Shen, Jie
3
2020
Error estimate of Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1427.76124
Chen, Hongtao; Mao, Jingjing; Shen, Jie
2
2020
Accurate and efficient spectral methods for elliptic PDEs in complex domains. Zbl 1440.65160
Gu, Yiqi; Shen, Jie
2
2020
An efficient and accurate numerical method for the spectral fractional Laplacian equation. Zbl 1433.65235
Chen, Sheng; Shen, Jie
1
2020
A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions. Zbl 1446.65128
Hu, Jingwei; Shen, Jie; Wang, Yingwei
1
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
1
2020
A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080
Shen, Jie; Xu, Jie; Yang, Jiang
148
2019
Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165
Li, Xiaoli; Shen, Jie; Rui, Hongxing
36
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
35
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
11
2019
An efficient space-time method for time fractional diffusion equation. Zbl 1466.65214
Shen, Jie; Sheng, Chang-Tao
8
2019
Stability and convergence analysis of rotational velocity correction methods for the Navier-Stokes equations. Zbl 1435.65119
Chen, Feng; Shen, Jie
5
2019
Efficient and accurate structure preserving schemes for complex nonlinear systems. Zbl 1446.65213
Shen, Jie
5
2019
Distributional compatibility for change of measures. Zbl 1420.60027
Shen, Jie; Shen, Yi; Wang, Bin; Wang, Ruodu
4
2019
Fast structured Jacobi-Jacobi transforms. Zbl 07040627
Shen, Jie; Wang, Yingwei; Xia, Jianlin
1
2019
Fundamental gaps of the fractional Schrödinger operator. Zbl 1429.35195
Bao, Weizhu; Ruan, Xinran; Shen, Jie; Sheng, Changtao
1
2019
The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181
Shen, Jie; Xu, Jie; Yang, Jiang
284
2018
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047
Shen, Jie; Xu, Jie
111
2018
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045
Cheng, Qing; Shen, Jie
47
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
19
2018
Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305
Mao, Zhiping; Shen, Jie
18
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
11
2018
Laguerre functions and their applications to tempered fractional differential equations on infinite intervals. Zbl 1398.65314
Chen, Sheng; Shen, Jie; Wang, Li-Lian
11
2018
Enriched spectral methods and applications to problems with weakly singular solutions. Zbl 1406.65123
Chen, Sheng; Shen, Jie
8
2018
A space-time Petrov-Galerkin spectral method for time fractional diffusion equation. Zbl 1438.65308
Sheng, Changtao; Shen, Jie
7
2018
A tight bound of hard thresholding. Zbl 1473.62287
Shen, Jie; Li, Ping
3
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
3
2018
Highly efficient and accurate spectral approximation of the angular Mathieu equation for any parameter values \(q\). Zbl 1424.65119
Alici, Haydar; Shen, Jie
2
2018
Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy. Zbl 1475.82027
Shen, Jie; Xu, Jie
2
2018
Approximations on \(\mathrm{SO}(3)\) by Wigner D-matrix and applications. Zbl 1398.65321
Shen, Jie; Xu, Jie; Zhang, Pingwen
1
2018
Preconditioning techniques in Chebyshev collocation method for elliptic equations. Zbl 1408.35025
Fang, Zhi-Wei; Shen, Jie; Sun, Hai-Wei
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
98
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
28
2017
Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075
Mao, Zhiping; Shen, Jie
19
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
17
2017
A hybrid spectral element method for fractional two-point boundary value problems. Zbl 1413.65307
Sheng, Changtao; Shen, Jie
12
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
9
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
5
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
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
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
1
2017
Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066
Chen, Sheng; Shen, Jie; Wang, Li-Lian
131
2016
On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059
Shen, Jie; Tang, Tao; Yang, Jiang
60
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
59
2016
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395
Mao, Zhiping; Shen, Jie
50
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
47
2016
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229
Chen, Ying; Shen, Jie
46
2016
Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. Zbl 1416.65482
Shen, Jie; Wang, Yingwei
15
2016
Efficient splitting schemes for magneto-hydrodynamic equations. Zbl 1388.76224
Choi, Heejun; Shen, Jie
10
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
10
2016
Two-phase Stefan problem with smoothed enthalpy. Zbl 1349.35433
Azaïez, M.; Jelassi, F.; Brahim, M. Mint; Shen, J.
1
2016
Efficient spectral-Galerkin method and analysis for elliptic PDEs with non-local boundary conditions. Zbl 1375.65159
Hu, Lina; Ma, Lina; Shen, Jie
1
2016
Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178
Shen, Jie; Yang, Xiaofeng
115
2015
Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184
Shen, Jie; Yang, Xiaofeng; Yu, Haijun
63
2015
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
49
2015
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078
Liu, Fei; Shen, Jie
23
2015
Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. Zbl 1349.65721
Shen, Jie; Sheng, Changtao; Wang, Zhongqing
17
2015
A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows. Zbl 1349.76198
Dong, S.; Shen, J.
16
2015
Dynamic transitions of quasi-geostrophic channel flow. Zbl 1329.35232
Dijkstra, Henk; Sengul, Taylan; Shen, Jie; Wang, Shouhong
14
2015
Pattern formations of 2D Rayleigh-Bénard convection with no-slip boundary conditions for the velocity at the critical length scales. Zbl 1333.76036
Sengul, Taylan; Shen, Jie; Wang, Shouhong
11
2015
Accurate solution and approximations of the linearized BGK equation for steady Couette flow. Zbl 1410.76412
Li, Wei; Luo, Li-Shi; Shen, Jie
5
2015
Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem. Zbl 1443.65306
An, Jing; Shen, Jie
5
2015
Spectral approximation of time-harmonic Maxwell equations in three-dimensional exterior domains. Zbl 1329.65286
Ma, Lina; Shen, Jie; Wang, Li-Lian
3
2015
Modeling and simulation of fingering pattern formation in a combustion model. Zbl 1318.80002
Hu, Lina; Brauner, Claude-Michel; Shen, Jie; Sivashinsky, Gregory I.
2
2015
A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates. Zbl 1488.65513
Mao, Zhiping; Shen, Jie
1
2015
Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057
Shen, Jie; Yang, Xiaofeng
45
2014
Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains. Zbl 1293.65161
Shen, Jie; Wang, Li-Lian; Yu, Haijun
11
2014
A new spectral method for numerical solution of the unbounded rough surface scattering problem. Zbl 1349.65646
He, Ying; Li, Peijun; Shen, Jie
7
2014
Unconditionally stable pressure-correction schemes for a linear fluid-structure interaction problem. Zbl 1324.76040
He, Ying; Shen, Jie
3
2014
Efficient spectral methods for transmission eigenvalues and estimation of the index of refraction. Zbl 1313.78022
An, Jing; Shen, Jie
3
2014
...and 130 more Documents
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Cited by 4,211 Authors

114 Shen, Jie
88 Yang, Xiaofeng
57 Guo, Ben-Yu
52 He, Yinnian
50 Wang, Cheng
44 Wang, Zhongqing
43 Wang, Lilian
41 Kim, Junseok
36 Wang, Qi
35 Feng, Xinlong
35 Wang, Yushun
33 Wise, Steven M.
31 Liu, Chun
30 Chen, Yanping
30 Dehghan Takht Fooladi, Mehdi
30 Zhao, Jia
29 Li, Huiyuan
27 Mei, Liquan
27 Xu, Chuanju
27 Zhang, Zhimin
26 Karniadakis, George Em
24 Chen, Wenbin
24 Gong, Yuezheng
24 Huang, Yunqing
24 Wang, Hong
23 Bhrawy, Ali Hassan
23 Doha, Eid H.
22 Nicholls, David P.
22 Tang, Tao
21 Du, Qiang
21 Guermond, Jean-Luc
21 Wang, Tianjun
21 Wang, Xiaoming
20 Bao, Weizhu
20 Han, Daozhi
20 Lee, Hyun Geun
20 Li, Xiaoli
20 Qiao, Zhonghua
19 Ju, Lili
18 Chen, Chuanjun
18 Miranville, Alain M.
18 Sun, Shuyu
18 Zaky, Mahmoud A.
17 Cai, Wenjun
17 Hou, Yanren
17 Li, Yibao
17 López, Juan Manuel
17 Ma, Heping
17 Parand, Kourosh
17 Yang, Junxiang
16 Cai, Yongyong
16 Chen, Lizhen
16 Dong, Suchuan
16 He, Xiaoming
16 Kou, Jisheng
16 Li, Jian
16 Wu, Boying
15 Li, Buyang
15 Lin, Ping
15 Liu, Wen-Jie
15 Marques, Francisco
15 Minev, Peter Dimitrov
15 Sherwin, Spencer J.
15 Yang, Jiang
14 Guillén González, Francisco M.
14 Jiang, Chaolong
14 Lowengrub, John Samuel
14 Mao, Zhiping
14 Wang, Quan
14 Yi, Lijun
13 An, Jing
13 Auteri, Franco
13 Codina, Ramon
13 Feng, James J.
13 Jia, Hongen
13 Li, Peijun
13 Yu, Haijun
13 Zhang, Luming
13 Zheng, Xiangcheng
12 Abd-Elhameed, Waleed Mohamed
12 An, Rong
12 Li, Xiao
12 Liu, Fawang
12 Liu, Zhengguang
12 Lu, Shujuan
12 Tachim Medjo, Theodore
12 Wang, Kun
12 Yue, Pengtao
12 Zhang, Zhengru
12 Zhou, Jianwei
11 Azaïez, Mejdi
11 Cheng, Qing
11 Grasselli, Maurizio
11 Lai, Mingchih
11 Liu, Hailiang
11 Si, Zhiyong
11 Yang, Yidu
11 Yu, Xuhong
10 Cheng, Kelong
10 Hafez, Ramy Mahmoud
...and 4,111 more Authors
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Cited in 306 Serials

509 Journal of Computational Physics
301 Journal of Scientific Computing
180 Applied Numerical Mathematics
154 Journal of Computational and Applied Mathematics
141 Computer Methods in Applied Mechanics and Engineering
123 Computers & Mathematics with Applications
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97 SIAM Journal on Scientific Computing
89 Journal of Fluid Mechanics
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29 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
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26 International Journal for Numerical Methods in Fluids
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20 Science China. Mathematics
19 Physica D
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18 Computer Physics Communications
17 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
17 Communications on Applied Mathematics and Computation
16 East Asian Journal on Applied Mathematics
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14 Abstract and Applied Analysis
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13 SIAM Journal on Applied Mathematics
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13 International Journal of Numerical Analysis and Modeling
13 Discrete and Continuous Dynamical Systems. Series S
11 BIT
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11 European Journal of Mechanics. B. Fluids
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10 Frontiers of Mathematics in China
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9 Applied Mathematics and Mechanics. (English Edition)
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9 International Journal of Numerical Methods for Heat & Fluid Flow
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7 ZAMP. Zeitschrift für angewandte Mathematik und Physik
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7 S\(\vec{\text{e}}\)MA Journal
7 AIMS Mathematics
6 Acta Mechanica
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6 International Journal of Nonlinear Sciences and Numerical Simulation
6 Multiscale Modeling & Simulation
6 Boundary Value Problems
6 SIAM/ASA Journal on Uncertainty Quantification
6 Journal of Function Spaces
5 Journal of Engineering Mathematics
5 Journal of Statistical Physics
5 Mathematical and Computer Modelling
5 SIAM Review
5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
4 International Journal of Engineering Science
4 Physica A
4 Bulletin of Mathematical Biology
4 Theoretical and Computational Fluid Dynamics
4 Journal of Approximation Theory
4 Acta Applicandae Mathematicae
4 Bulletin of the Iranian Mathematical Society
4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
4 RAIRO. Modélisation Mathématique et Analyse Numérique
4 Calculus of Variations and Partial Differential Equations
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