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Shen, Jie

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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: 244 Publications since 1988, including 3 Books
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Co-Authors

27 single-authored
22 Wang, Lilian
21 Yang, Xiaofeng
15 Liu, Chun
10 Guo, Ben-Yu
8 Xu, Chuanju
8 Yu, Haijun
7 Chen, Feng
7 Feng, James J.
7 Guermond, Jean-Luc
7 López, Juan Manuel
7 Sheng, Changtao
6 Cheng, Qing
6 Marques, Francisco
6 Xu, Jie
6 Yue, Pengtao
5 An, Jing
5 Wang, Qi
5 Wang, Shouhong
5 Wang, Yingwei
4 Bao, Weizhu
4 Chen, Lizhen
4 Li, Xiaoli
4 Ma, Lina
4 Mao, Zhiping
4 Nicholls, David P.
4 Tang, Tao
4 Temam, Roger Meyer
4 Wang, Zhongqing
4 Zhuang, Qingqu
3 Cai, Yongyong
3 Forest, M. Gregory
3 Gu, Yiqi
3 He, Ying
3 Li, Huiyuan
3 Wise, Steven M.
3 Yang, Jiang
2 Alici, Haydar
2 Azaïez, Mejdi
2 Chen, Hongtao
2 Choi, Heejun
2 Fang, Qirong
2 Hu, Lina
2 Huang, Fukeng
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, Ruodu
2 Wang, Xiaoming
2 Wu, Jiahong
2 Xia, Jianlin
2 Xiu, Dongbin
2 Xu, Chenglong
2 Yang, Zhiguo
2 Yuan, Juanming
2 Zhao, Jia
1 Brahim, M. Mint
1 Brauner, Claude-Michel
1 Cai, Jiaxiang
1 Cao, Duo
1 Chandy, Abhilash J.
1 Chen, Falai
1 Chen, Jia
1 Chen, Zhi
1 Cheng, Ting
1 Colbert-Kelly, Sean
1 Cui, Zhenlu
1 Dai, C. M.
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
1 Hart, John E.
1 He, Xiaoming
1 He, Youguo
1 Hu, Jingwei
1 Hu, Wencheng
1 Huang, Wenhua
1 Jelassi, Faten
1 Jian, Jun
1 Jiang, Xingrui
...and 56 more Co-Authors
all top 5

Serials

32 Journal of Computational Physics
24 SIAM Journal on Numerical Analysis
22 Journal of Scientific Computing
20 SIAM Journal on Scientific Computing
9 Mathematics of Computation
9 Applied Numerical Mathematics
8 Communications in Computational Physics
7 Numerische Mathematik
5 Computer Methods in Applied Mechanics and Engineering
5 Journal of Fluid Mechanics
5 Advances in Computational Mathematics
5 Discrete and Continuous Dynamical Systems
5 Numerical Mathematics: Theory, Methods and Applications
4 Journal of Computational and Applied Mathematics
4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
4 Discrete and Continuous Dynamical Systems. Series B
4 Communications in Mathematical Sciences
3 Mathematical Methods in the Applied Sciences
3 Physica D
3 Mathematical Problems in Engineering
3 Journal of Mathematical Study
3 International Journal of Numerical Analysis and Modeling
3 East Asian Journal on Applied Mathematics
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 Journal of Non-Newtonian Fluid Mechanics
2 Physics of Fluids
1 Applicable Analysis
1 Computers and Fluids
1 Computers & Mathematics with Applications
1 Computer Physics Communications
1 IMA Journal of Numerical Analysis
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 Machine Learning
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 Journal of Liaoning Normal University. Natural Science Edition
1 IEEE Transactions on Image Processing
1 Foundations of Computational Mathematics
1 Journal of Machine Learning Research (JMLR)
1 Multiscale Modeling & Simulation
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

202 Publications have been cited 6,192 times in 2,942 Documents Cited by Year
An overview of projection methods for incompressible flows. Zbl 1122.76072
Guermond, J. L.; Minev, P.; Shen, Jie
353
2006
Spectral methods. Algorithms, analysis and applications. Zbl 1227.65117
Shen, Jie; Tang, Tao; Wang, Li-Lian
264
2011
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Zbl 1201.65184
Shen, Jie; Yang, Xiaofeng
250
2010
Efficient spectral-Galerkin method. I: Direct solvers of second- and fourth-order equations using Legendre polynomials. Zbl 0811.65097
Shen, Jie
247
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
192
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
188
2004
Spectral and high-order methods with applications. Zbl 1234.65005
Shen, Jie; Tang, Tao
176
2006
The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181
Shen, Jie; Xu, Jie; Yang, Jiang
161
2018
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.
130
2012
On error estimates of projection methods for Navier-Stokes equations: First-order schemes. Zbl 0741.76051
Shen, Jie
114
1992
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
110
2010
Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066
Chen, Sheng; Shen, Jie; Wang, Li-Lian
109
2016
Efficient spectral-Galerkin method. II: Direct solvers of second- and fourth-order equations using Chebyshev polynomials. Zbl 0840.65113
Shen, Jie
101
1995
Applications of semi-implicit Fourier-spectral method to phase field equations. Zbl 1017.65533
Chen, L. Q.; Shen, Jie
98
1998
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
92
2006
On the error estimates for the rotational pressure-correction projection methods. Zbl 1093.76050
Guermond, J. L.; Shen, Jie
89
2004
Stable and efficient spectral methods in unbounded domains using Laguerre functions. Zbl 0979.65105
Shen, Jie
87
2000
Velocity-correction projection methods for incompressible flows. Zbl 1130.76395
Guermond, J. L.; Shen, Jie
87
2003
On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes. Zbl 0855.76049
Shen, Jie
84
1996
Long time stability and convergence for fully discrete nonlinear Galerkin methods. Zbl 0684.65095
Shen, Jie
82
1990
Optimal spectral-Galerkin methods using generalized Jacobi polynomials. Zbl 1102.76047
Guo, Benyu; Shen, Jie; Wang, Li-Lian
76
2006
On error estimates of the penalty method for unsteady Navier-Stokes equations. Zbl 0822.35008
Shen, Jie
71
1995
Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178
Shen, Jie; Yang, Xiaofeng
71
2015
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
70
2017
Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Zbl 0969.65094
Guo, Ben-Yu; Shen, Jie
69
2000
A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080
Shen, Jie; Xu, Jie; Yang, Jiang
67
2019
Some recent advances on spectral methods for unbounded domains. Zbl 1364.65265
Shen, Jie; Wang, Li-Lian
63
2009
A new class of truly consistent splitting schemes for incompressible flows. Zbl 1032.76529
Guermond, J. L.; Shen, Jie
63
2003
A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. Zbl 1084.35083
Bao, Weizhu; Shen, Jie
59
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
57
2003
Hopf bifurcation of the unsteady regularized driven cavity flow. Zbl 0725.76059
Shen, Jie
52
1991
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047
Shen, Jie; Xu, Jie
51
2018
Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations. Zbl 1382.65222
Mao, Zhiping; Chen, Sheng; Shen, Jie
50
2016
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.
50
2012
A rational approximation and its applications to differential equations on the half line. Zbl 0984.65104
Guo, Benyu; Shen, Jie; Wang, Zhongqing
49
2000
Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Zbl 1400.65049
Shen, Jie; Yang, Xiaofeng
48
2010
Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184
Shen, Jie; Yang, Xiaofeng; Yu, Haijun
47
2015
Efficient spectral-Galerkin methods. III: Polar and cylindrical geometries. Zbl 0890.65117
Shen, Jie
47
1997
Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Zbl 1118.65111
Shen, Jie; Wang, Li-Lian
42
2007
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395
Mao, Zhiping; Shen, Jie
41
2016
Generalized Jacobi polynomials/functions and their applications. Zbl 1171.33006
Guo, Ben-Yu; Shen, Jie; Wang, Li-Lian
40
2009
An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161
Collins, Craig; Shen, Jie; Wise, Steven M.
39
2013
On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059
Shen, Jie; Tang, Tao; Yang, Jiang
39
2016
Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1109.76037
Pyo, Jae-Hong; Shen, Jie
38
2007
Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems. Zbl 1388.65117
Chen, Feng; Shen, Jie
36
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.
36
2005
Spectral and pseudospectral approximations using Hermite functions: Application to the Dirac equation. Zbl 1032.33004
Guo, Ben-yu; Shen, Jie; Xu, Cheng-long
36
2003
Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057
Shen, Jie; Yang, Xiaofeng
35
2014
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229
Chen, Ying; Shen, Jie
35
2016
Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval. Zbl 1001.65129
Guo, Benyu; Shen, Jie; Wang, Zhongqing
35
2002
An efficient moving mesh spectral method for the phase-field model of two-phase flows. Zbl 1159.76032
Shen, Jie; Yang, Xiaofeng
35
2009
An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. I: Axisymmetric cases. Zbl 0908.76068
Lopez, J. M.; Shen, Jie
34
1998
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
33
2015
On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0782.76025
Shen, Jie
32
1992
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
32
2005
Efficient stochastic Galerkin methods for random diffusion equations. Zbl 1161.65008
Xiu, Dongbin; Shen, Jie
32
2009
Efficient spectral sparse grid methods and applications to high-dimensional elliptic problems. Zbl 1233.65094
Shen, Jie; Yu, Haijun
31
2010
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
30
2016
Remarks on the pressure error estimates for the projection methods. Zbl 0802.76060
Shen, Jie
30
1994
Pressure boundary condition for the time-dependent incompressible Navier-Stokes equations. Zbl 1155.76322
Sani, R. L.; Shen, J.; Pironneau, O.; Gresho, P. M.
30
2006
Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains. Zbl 1154.65082
Shen, Jie; Wang, Li-Lian
27
2007
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
27
2005
Spectral approximation of the Helmholtz equation with high wave numbers. Zbl 1091.65119
Shen, Jie; Wang, Li-Lian
26
2005
Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
26
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
26
2009
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045
Cheng, Qing; Shen, Jie
26
2018
Mass and volume conservation in phase field models for binary fluids. Zbl 1373.76317
Shen, Jie; Yang, Xiaofeng; Wang, Qi
24
2013
A stable high-order method for two-dimensional bounded-obstacle scattering. Zbl 1130.78007
Nicholls, David P.; Shen, Jie
23
2006
A spectral-element method for transmission eigenvalue problems. Zbl 1292.65119
An, Jing; Shen, Jie
22
2013
Generalized Laguerre approximation and its applications to exterior problems. Zbl 1073.65130
Guo, Benyu; Shen, Jie; Xu, Chenglong
22
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
22
2001
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
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
22
2002
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
22
2019
On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0739.76017
Shen, Jie
21
1992
A triangular spectral element method using fully tensorial rational basis functions. Zbl 1197.65187
Shen, Jie; Wang, Li-Lian; Li, Huiyuan
21
2009
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. Zbl 1123.76049
Fang, Qirong; Nicholls, David P.; Shen, Jie
21
2007
An efficient spectral method for acoustic scattering from rough surfaces. Zbl 1164.65303
Xiu, Dongbin; Shen, Jie
21
2007
Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. Zbl 1215.65179
Shen, Jie; Wang, Li-Lian
21
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
20
2013
Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. Zbl 1380.65203
Cheng, Qing; Yang, Xiaofeng; Shen, Jie
20
2017
Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165
Li, Xiaoli; Shen, Jie; Rui, Hongxing
20
2019
On numerical approximations of forward-backward stochastic differential equations. Zbl 1177.60064
Ma, Jin; Shen, Jie; Zhao, Yanhong
20
2008
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.
18
2002
Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle. Zbl 1197.65176
Li, Huiyuan; Shen, Jie
18
2010
An unconditionally stable rotational velocity-correction scheme for incompressible flows. Zbl 1425.76058
Dong, S.; Shen, J.
17
2010
On liquid crystal flows with free-slip boundary conditions. Zbl 1014.76005
Liu, Chun; Shen, Jie
16
2001
Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422
Liu, Chun; Shen, Jie; Yang, Xiaofeng
16
2007
On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval. Zbl 1157.35093
Goubet, Olivier; Shen, Jie
16
2007
Legendre and Chebyshev dual-Petrov-Galerkin methods for hyperbolic equations. Zbl 1173.65342
Shen, Jie; Wang, Li-Lian
16
2007
A rigorous numerical analysis of the transformed field expansion method. Zbl 1410.65465
Nicholls, David P.; Shen, Jie
15
2009
A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates. Zbl 1149.76039
Bao, Weizhu; Shen, Jie
15
2008
Shear cell rupture of nematic liquid crystal droplets in viscous fluids. Zbl 1282.76061
Yang, Xiaofeng; Forest, M. Gregory; Liu, Chun; Shen, Jie
14
2011
Convergence of approximate attractors for a fully discrete system for reaction-diffusion equations. Zbl 0715.65074
Shen, Jie
14
1989
On a new pseudocompressibility method for the incompressible Navier-Stokes equations. Zbl 0853.76052
Shen, Jie
14
1996
An efficient direct parallel spectral-element solver for separable elliptic problems. Zbl 1123.65116
Kwan, Yuen-Yick; Shen, Jie
14
2007
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078
Liu, Fei; Shen, Jie
14
2015
Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075
Mao, Zhiping; Shen, Jie
13
2017
Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. Zbl 1349.65721
Shen, Jie; Sheng, Changtao; Wang, Zhongqing
13
2015
Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. Zbl 1416.65482
Shen, Jie; Wang, Yingwei
13
2016
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
9
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
6
2020
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294
Li, Xiaoli; Shen, Jie
6
2020
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437
Cai, Jiaxiang; Shen, Jie
5
2020
Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. Zbl 1440.65192
Chen, Hongtao; Mao, Jingjing; Shen, Jie
4
2020
Unconditionally bound preserving and energy dissipative schemes for a class of Keller-Segel equations. Zbl 1440.65101
Shen, Jie; Xu, Jie
4
2020
Global constraints preserving scalar auxiliary variable schemes for gradient flows. Zbl 1456.65087
Cheng, Qing; 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
A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210
Huang, Fukeng; Shen, Jie; Yang, Zhiguo
2
2020
Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167
Li, Xiaoli; Shen, Jie
1
2020
Bound preserving and energy dissipative schemes for porous medium equation. Zbl 1436.65101
Gu, Yiqi; Shen, Jie
1
2020
A spectrally accurate approximation to subdiffusion equations using the log orthogonal functions. Zbl 1434.65291
Chen, Sheng; Shen, Jie; Zhang, Zhimin; Zhou, Zhi
1
2020
Accurate and efficient spectral methods for elliptic PDEs in complex domains. Zbl 1440.65160
Gu, Yiqi; Shen, Jie
1
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 07345498
Li, Xiaoli; Shen, Jie
1
2020
A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080
Shen, Jie; Xu, Jie; Yang, Jiang
67
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
22
2019
Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165
Li, Xiaoli; Shen, Jie; Rui, Hongxing
20
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
4
2019
Distributional compatibility for change of measures. Zbl 1420.60027
Shen, Jie; Shen, Yi; Wang, Bin; Wang, Ruodu
3
2019
An efficient space-time method for time fractional diffusion equation. Zbl 1466.65214
Shen, Jie; Sheng, Chang-Tao
2
2019
Fast structured Jacobi-Jacobi transforms. Zbl 07040627
Shen, Jie; Wang, Yingwei; Xia, Jianlin
1
2019
Efficient and accurate structure preserving schemes for complex nonlinear systems. Zbl 1446.65213
Shen, Jie
1
2019
The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181
Shen, Jie; Xu, Jie; Yang, Jiang
161
2018
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047
Shen, Jie; Xu, Jie
51
2018
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045
Cheng, Qing; Shen, Jie
26
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
13
2018
Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305
Mao, Zhiping; Shen, Jie
12
2018
Laguerre functions and their applications to tempered fractional differential equations on infinite intervals. Zbl 1398.65314
Chen, Sheng; Shen, Jie; Wang, Li-Lian
9
2018
Enriched spectral methods and applications to problems with weakly singular solutions. Zbl 1406.65123
Chen, Sheng; Shen, Jie
6
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
6
2018
A space-time Petrov-Galerkin spectral method for time fractional diffusion equation. Zbl 1438.65308
Sheng, Changtao; Shen, Jie
5
2018
A tight bound of hard thresholding. Zbl 06982964
Shen, Jie; Li, Ping
3
2018
Approximations on \(\mathrm{SO}(3)\) by Wigner D-matrix and applications. Zbl 1398.65321
Shen, Jie; Xu, Jie; Zhang, Pingwen
1
2018
Wavenumber explicit analysis for time-harmonic Maxwell equations in a spherical shell and spectral approximations. Zbl 06983832
Ma, Lina; Shen, Jie; Wang, Li-Lian; Yang, Zhiguo
1
2018
Highly efficient and accurate spectral approximation of the angular Mathieu equation for any parameter values \(q\). Zbl 1424.65119
Alici, Haydar; Shen, Jie
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
70
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
20
2017
Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075
Mao, Zhiping; Shen, Jie
13
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
11
2017
A hybrid spectral element method for fractional two-point boundary value problems. Zbl 1413.65307
Sheng, Changtao; Shen, Jie
8
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
8
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
4
2017
Online optimization for max-norm regularization. Zbl 1454.68132
Shen, Jie; Xu, Huan; Li, Ping
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
1
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
109
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
50
2016
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395
Mao, Zhiping; Shen, Jie
41
2016
On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059
Shen, Jie; Tang, Tao; Yang, Jiang
39
2016
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229
Chen, Ying; Shen, Jie
35
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
30
2016
Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. Zbl 1416.65482
Shen, Jie; Wang, Yingwei
13
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
8
2016
Efficient splitting schemes for magneto-hydrodynamic equations. Zbl 1388.76224
Choi, Heejun; Shen, Jie
5
2016
Two-phase Stefan problem with smoothed enthalpy. Zbl 1349.35433
Azaïez, M.; Jelassi, F.; Brahim, M. Mint; Shen, J.
1
2016
Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178
Shen, Jie; Yang, Xiaofeng
71
2015
Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184
Shen, Jie; Yang, Xiaofeng; Yu, Haijun
47
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
33
2015
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078
Liu, Fei; Shen, Jie
14
2015
Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. Zbl 1349.65721
Shen, Jie; Sheng, Changtao; Wang, Zhongqing
13
2015
Dynamic transitions of quasi-geostrophic channel flow. Zbl 1329.35232
Dijkstra, Henk; Sengul, Taylan; Shen, Jie; Wang, Shouhong
11
2015
A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows. Zbl 1349.76198
Dong, S.; Shen, J.
9
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
8
2015
Accurate solution and approximations of the linearized BGK equation for steady Couette flow. Zbl 1410.76412
Li, Wei; Luo, Li-Shi; Shen, Jie
4
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.
1
2015
Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem. Zbl 1443.65306
An, Jing; Shen, Jie
1
2015
Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057
Shen, Jie; Yang, Xiaofeng
35
2014
Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains. Zbl 1293.65161
Shen, Jie; Wang, Li-Lian; Yu, Haijun
8
2014
A new spectral method for numerical solution of the unbounded rough surface scattering problem. Zbl 1349.65646
He, Ying; Li, Peijun; Shen, Jie
6
2014
Efficient spectral methods for transmission eigenvalues and estimation of the index of refraction. Zbl 1313.78022
An, Jing; Shen, Jie
3
2014
Unconditionally stable pressure-correction schemes for a linear fluid-structure interaction problem. Zbl 1324.76040
He, Ying; Shen, Jie
2
2014
Parallel spectral-element direction splitting method for incompressible Navier-Stokes equations. Zbl 1291.76233
Chen, Lizhen; Shen, Jie; Xu, Chuanju; Luo, Li-Shi
1
2014
An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161
Collins, Craig; Shen, Jie; Wise, Steven M.
39
2013
Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems. Zbl 1388.65117
Chen, Feng; Shen, Jie
36
2013
Mass and volume conservation in phase field models for binary fluids. Zbl 1373.76317
Shen, Jie; Yang, Xiaofeng; Wang, Qi
24
2013
A spectral-element method for transmission eigenvalue problems. Zbl 1292.65119
An, Jing; Shen, Jie
22
2013
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
20
2013
Error analysis of the Strang time-splitting Laguerre-Hermite/Hermite collocation methods for the Gross-Pitaevskii equation. Zbl 1264.65168
Shen, Jie; Wang, Zhong-Qing
7
2013
A GPU parallelized spectral method for elliptic equations in rectangular domains. Zbl 1349.65641
Chen, Feng; Shen, Jie
3
2013
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.
130
2012
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.
50
2012
Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications. Zbl 1250.65138
Chen, Feng; Shen, Jie
13
2012
A new spectral element method for pricing European options under the Black-Scholes and Merton jump diffusion models. Zbl 1254.91745
Chen, Feng; Shen, Jie; Yu, Haijun
10
2012
An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure. Zbl 1243.78025
He, Ying; Nicholls, David P.; Shen, Jie
9
2012
Analysis of the scattering by an unbounded rough surface. Zbl 1288.78020
Li, Peijun; Shen, Jie
9
2012
A unstructured nodal spectral-element method for the Navier-Stokes equations. Zbl 1373.76024
Chen, Lizhen; Shen, Jie; Xu, Chuanju
8
2012
Efficient spectral sparse grid methods and applications to high-dimensional elliptic equations II. Unbounded domains. Zbl 1269.65130
Shen, Jie; Yu, Haijun
6
2012
On the approximation of the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model. I: A new weighted formulation and an optimal spectral-Galerkin algorithm in two dimensions. Zbl 1250.82033
Shen, Jie; Yu, Haijun
3
2012
Spectral methods. Algorithms, analysis and applications. Zbl 1227.65117
Shen, Jie; Tang, Tao; Wang, Li-Lian
264
2011
Shear cell rupture of nematic liquid crystal droplets in viscous fluids. Zbl 1282.76061
Yang, Xiaofeng; Forest, M. Gregory; Liu, Chun; Shen, Jie
14
2011
A triangular spectral method for the Stokes equations. Zbl 1249.65262
Chen, Lizhen; Shen, Jie; Xu, Chuanju
8
2011
Spectral direction splitting schemes for the incompressible Navier-Stokes equations. Zbl 1302.76135
Chen, Lizhen; Shen, Jie; Xu, Chuanju
6
2011
A pressure-correction scheme for rotational Navier-Stokes equations and its application to rotating turbulent flows. Zbl 1364.52010
Shetty, Dinesh A.; Shen, Jie; Chandy, Abhilash J.; Frankel, Steven H.
4
2011
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Zbl 1201.65184
Shen, Jie; Yang, Xiaofeng
250
2010
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
110
2010
Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Zbl 1400.65049
Shen, Jie; Yang, Xiaofeng
48
2010
Efficient spectral sparse grid methods and applications to high-dimensional elliptic problems. Zbl 1233.65094
Shen, Jie; Yu, Haijun
31
2010
Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. Zbl 1215.65179
Shen, Jie; Wang, Li-Lian
21
2010
Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle. Zbl 1197.65176
Li, Huiyuan; Shen, Jie
18
2010
...and 102 more Documents
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Cited by 3,567 Authors

105 Shen, Jie
67 Yang, Xiaofeng
56 Guo, Ben-Yu
46 He, Yinnian
40 Wang, Lilian
38 Wang, Zhongqing
36 Wang, Cheng
33 Wang, Qi
27 Feng, Xinlong
26 Dehghan Takht Fooladi, Mehdi
26 Wang, Yushun
25 Liu, Chun
24 Kim, Junseok
24 Wise, Steven M.
24 Zhao, Jia
23 Bhrawy, Ali Hassan
23 Mei, Liquan
22 Chen, Yanping
22 Doha, Eid H.
22 Karniadakis, George Em
22 Li, Huiyuan
21 Guermond, Jean-Luc
21 Wang, Hong
20 Gong, Yuezheng
20 Zhang, Zhimin
19 Du, Qiang
18 Nicholls, David P.
18 Tang, Tao
18 Wang, Xiaoming
17 Bao, Weizhu
17 Chen, Wenbin
17 Huang, Yunqing
17 Wang, Tianjun
16 López, Juan Manuel
16 Ma, Heping
16 Miranville, Alain M.
16 Parand, Kourosh
16 Qiao, Zhonghua
16 Xu, Chuanju
15 Han, Daozhi
15 Lee, Hyun Geun
15 Li, Jian
15 Minev, Peter Dimitrov
15 Sun, Shuyu
14 Kou, Jisheng
14 Marques, Francisco
13 Chen, Lizhen
13 Guillén González, Francisco M.
13 Hou, Yanren
13 Ju, Lili
13 Li, Xiaoli
13 Liu, Wen-Jie
13 Lowengrub, John Samuel
13 Mao, Zhiping
13 Sherwin, Spencer J.
13 Wu, Boying
13 Yi, Lijun
12 An, Rong
12 Auteri, Franco
12 Cai, Yongyong
12 Feng, James J.
12 Zhou, Jianwei
11 Abd-Elhameed, Waleed Mohamed
11 Chen, Chuanjun
11 Codina, Ramon
11 Dong, Suchuan
11 He, Xiaoming
11 Li, Buyang
11 Lin, Ping
11 Liu, Fawang
11 Lu, Shujuan
11 Yu, Haijun
11 Yue, Pengtao
11 Zaky, Mahmoud A.
11 Zhang, Luming
10 An, Jing
10 Grasselli, Maurizio
10 Jiang, Chaolong
10 Tachim Medjo, Theodore
10 Wang, Quan
10 Yu, Xuhong
10 Zhang, Chao
10 Zheng, Xiangcheng
9 Cai, Wenjun
9 Hafez, Ramy Mahmoud
9 Jiang, Xiaoyun
9 Li, Kaitai
9 Li, Yibao
9 Mokhtary, Payam
9 Salgado, Abner J.
9 Si, Zhiyong
9 Wu, Hao
9 Yang, Yidu
8 Blackburn, Hugh M.
8 Chen, Zhangxin
8 Cheng, Kelong
8 de Frutos, Javier
8 Dong, Xuanchun
8 Han, Jiayu
8 Hong, Youngjoon
...and 3,467 more Authors
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Cited in 266 Serials

415 Journal of Computational Physics
252 Journal of Scientific Computing
160 Applied Numerical Mathematics
136 Journal of Computational and Applied Mathematics
112 Computer Methods in Applied Mechanics and Engineering
107 Computers & Mathematics with Applications
94 Computers and Fluids
85 SIAM Journal on Scientific Computing
82 Applied Mathematics and Computation
79 Journal of Fluid Mechanics
59 Mathematics of Computation
56 SIAM Journal on Numerical Analysis
48 Advances in Computational Mathematics
46 Numerical Algorithms
42 Numerische Mathematik
38 Mathematical Methods in the Applied Sciences
35 Numerical Methods for Partial Differential Equations
35 Applied Mathematics Letters
35 Physics of Fluids
32 International Journal of Computer Mathematics
29 Discrete and Continuous Dynamical Systems. Series B
28 Journal of Mathematical Analysis and Applications
26 International Journal for Numerical Methods in Fluids
25 Applied Mathematical Modelling
25 Communications in Nonlinear Science and Numerical Simulation
24 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
21 Computational and Applied Mathematics
21 Advances in Applied Mathematics and Mechanics
19 Mathematical Problems in Engineering
18 Computer Physics Communications
16 Science China. Mathematics
15 Physica D
14 Journal of Differential Equations
14 Abstract and Applied Analysis
14 East Asian Journal on Applied Mathematics
13 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
11 Calcolo
10 SIAM Journal on Applied Mathematics
10 Engineering Analysis with Boundary Elements
10 Nonlinear Dynamics
10 Advances in Difference Equations
10 Frontiers of Mathematics in China
9 Archive for Rational Mechanics and Analysis
9 BIT
9 International Journal for Numerical Methods in Engineering
9 Mathematics and Computers in Simulation
9 Numerical Functional Analysis and Optimization
9 Applied Mathematics and Mechanics. (English Edition)
9 Journal of Non-Newtonian Fluid Mechanics
9 International Journal of Numerical Methods for Heat & Fluid Flow
9 Discrete and Continuous Dynamical Systems
9 Journal of Mathematical Fluid Mechanics
9 Comptes Rendus. Mathématique. Académie des Sciences, Paris
9 Communications on Applied Mathematics and Computation
8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
8 Fractional Calculus & Applied Analysis
8 European Journal of Mechanics. B. Fluids
8 Nonlinear Analysis. Real World Applications
8 Computational Methods in Applied Mathematics
8 Journal of Applied Mathematics
8 Discrete and Continuous Dynamical Systems. Series S
7 Applicable Analysis
7 ZAMP. Zeitschrift für angewandte Mathematik und Physik
7 Chaos, Solitons and Fractals
7 Chinese Annals of Mathematics. Series B
7 Communications on Pure and Applied Analysis
7 International Journal of Computational Methods
6 Computational Mechanics
6 SIAM Journal on Mathematical Analysis
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6 Journal of Applied Mathematics and Computing
6 S\(\vec{\text{e}}\)MA Journal
6 SIAM/ASA Journal on Uncertainty Quantification
5 Journal of Statistical Physics
5 Mathematical and Computer Modelling
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
5 Multiscale Modeling & Simulation
5 Boundary Value Problems
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 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
4 RAIRO. Modélisation Mathématique et Analyse Numérique
4 Calculus of Variations and Partial Differential Equations
4 Numerical Linear Algebra with Applications
4 Mathematical Modelling and Analysis
4 Journal of Theoretical Biology
4 Research in the Mathematical Sciences
3 Acta Mechanica
3 Journal of the Mechanics and Physics of Solids
3 Nonlinearity
3 SIAM Journal on Control and Optimization
3 Bulletin of the Iranian Mathematical Society
3 Acta Mathematicae Applicatae Sinica. English Series
3 Asymptotic Analysis
3 Applications of Mathematics
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Cited in 49 Fields

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