Edit Profile (opens in new tab) Shen, Jie Co-Author Distance Author ID: shen.jie Published as: Shen, Jie; Shen, J. External Links: MGP Documents Indexed: 296 Publications since 1988, including 2 Books and 12 Additional arXiv Preprints 5 Contributions as Editor Biographic References: 1 Publication Co-Authors: 118 Co-Authors with 207 Joint Publications 4,809 Co-Co-Authors all top 5 Co-Authors 29 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 Kwan, Yuen-Yick 2 Li, Peijun 2 Lin, Guang 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, Jiahao 2 Zhang, Shiheng 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. ...and 110 more Co-Authors all top 5 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. 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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 all top 5 Fields 222 Numerical analysis (65-XX) 139 Partial differential equations (35-XX) 110 Fluid mechanics (76-XX) 16 Approximations and expansions (41-XX) 14 Statistical mechanics, structure of matter (82-XX) 11 Computer science (68-XX) 11 Optics, electromagnetic theory (78-XX) 9 Special functions (33-XX) 8 Ordinary differential equations (34-XX) 8 Probability theory and stochastic processes (60-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Biology and other natural sciences (92-XX) 6 Real functions (26-XX) 6 Operations research, mathematical programming (90-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Quantum theory (81-XX) 4 General and overarching topics; collections (00-XX) 4 Geophysics (86-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Statistics (62-XX) 3 Mechanics of deformable solids (74-XX) 3 Information and communication theory, circuits (94-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 250 Publications have been cited 10,490 times in 4,733 Documents Cited by ▼ Year ▼ Spectral methods. Algorithms, analysis and applications. Zbl 1227.65117 Shen, Jie; Tang, Tao; Wang, Li-Lian 735 2011 An overview of projection methods for incompressible flows. Zbl 1122.76072 Guermond, J. L.; Minev, P.; Shen, Jie 544 2006 Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Zbl 1201.65184 Shen, Jie; Yang, Xiaofeng 500 2010 The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181 Shen, Jie; Xu, Jie; Yang, Jiang 474 2018 Efficient spectral-Galerkin method. I: Direct solvers of second- and fourth-order equations using Legendre polynomials. Zbl 0811.65097 Shen, Jie 319 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 301 2003 A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080 Shen, Jie; Xu, Jie; Yang, Jiang 287 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 272 2004 Spectral and high-order methods with applications. Zbl 1234.65005 Shen, Jie; Tang, Tao 261 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. 254 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 187 2010 Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047 Shen, Jie; Xu, Jie 177 2018 Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066 Chen, Sheng; Shen, Jie; Wang, Li-Lian 162 2016 Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178 Shen, Jie; Yang, Xiaofeng 161 2015 On error estimates of projection methods for Navier-Stokes equations: First-order schemes. Zbl 0741.76051 Shen, Jie 155 1992 Applications of semi-implicit Fourier-spectral method to phase field equations. Zbl 1017.65533 Chen, L. Q.; Shen, Jie 145 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 141 2017 On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes. Zbl 0855.76049 Shen, Jie 128 1996 On the error estimates for the rotational pressure-correction projection methods. Zbl 1093.76050 Guermond, J. L.; Shen, Jie 128 2004 Velocity-correction projection methods for incompressible flows. Zbl 1130.76395 Guermond, J. L.; Shen, Jie 122 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 119 2006 Efficient spectral-Galerkin method. II: Direct solvers of second- and fourth-order equations using Chebyshev polynomials. Zbl 0840.65113 Shen, Jie 112 1995 Long time stability and convergence for fully discrete nonlinear Galerkin methods. Zbl 0684.65095 Shen, Jie 110 1990 Stable and efficient spectral methods in unbounded domains using Laguerre functions. Zbl 0979.65105 Shen, Jie 100 2000 On error estimates of the penalty method for unsteady Navier-Stokes equations. Zbl 0822.35008 Shen, Jie 98 1995 On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059 Shen, Jie; Tang, Tao; Yang, Jiang 95 2016 Optimal spectral-Galerkin methods using generalized Jacobi polynomials. Zbl 1102.76047 Guo, Benyu; Shen, Jie; Wang, Li-Lian 92 2006 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 Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Zbl 1400.65049 Shen, Jie; Yang, Xiaofeng 84 2010 Some recent advances on spectral methods for unbounded domains. Zbl 1364.65265 Shen, Jie; Wang, Li-Lian 83 2009 A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. Zbl 1084.35083 Bao, Weizhu; Shen, Jie 82 2005 A new class of truly consistent splitting schemes for incompressible flows. Zbl 1032.76529 Guermond, J. L.; Shen, Jie 79 2003 A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KdV equation. Zbl 1053.65085 Shen, Jie 77 2003 Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184 Shen, Jie; Yang, Xiaofeng; Yu, Haijun 77 2015 Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Zbl 0969.65094 Guo, Ben-Yu; Shen, Jie 76 2000 Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229 Chen, Ying; Shen, Jie 75 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 72 2016 Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165 Li, Xiaoli; Shen, Jie; Rui, Hongxing 71 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 69 2015 Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057 Shen, Jie; Yang, Xiaofeng 69 2014 Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045 Cheng, Qing; Shen, Jie 69 2018 Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1109.76037 Pyo, Jae-Hong; Shen, Jie 63 2007 Efficient spectral-Galerkin methods. III: Polar and cylindrical geometries. Zbl 0890.65117 Shen, Jie 61 1997 Hopf bifurcation of the unsteady regularized driven cavity flow. Zbl 0725.76059 Shen, Jie 61 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 61 2016 A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211 Cheng, Qing; Liu, Chun; Shen, Jie 60 2020 Generalized Jacobi polynomials/functions and their applications. Zbl 1171.33006 Guo, Ben-Yu; Shen, Jie; Wang, Li-Lian 59 2009 Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395 Mao, Zhiping; Shen, Jie 59 2016 Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Zbl 1118.65111 Shen, Jie; Wang, Li-Lian 58 2007 A rational approximation and its applications to differential equations on the half line. Zbl 0984.65104 Guo, Benyu; Shen, Jie; Wang, Zhongqing 57 2000 An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161 Collins, Craig; Shen, Jie; Wise, Steven M. 53 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 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 52 2019 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 50 2009 A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210 Huang, Fukeng; Shen, Jie; Yang, Zhiguo 49 2020 Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval. Zbl 1001.65129 Guo, Benyu; Shen, Jie; Wang, Zhongqing 48 2002 Spectral and pseudospectral approximations using Hermite functions: Application to the Dirac equation. Zbl 1032.33004 Guo, Ben-yu; Shen, Jie; Xu, Cheng-long 47 2003 Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems. Zbl 1388.65117 Chen, Feng; Shen, Jie 47 2013 On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0782.76025 Shen, Jie 45 1992 Efficient stochastic Galerkin methods for random diffusion equations. Zbl 1161.65008 Xiu, Dongbin; Shen, Jie 45 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 The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems. Zbl 1484.65196 Shen, Jie; Yang, Xiaofeng 41 2020 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 Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120 Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie 39 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 38 2001 Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167 Li, Xiaoli; Shen, Jie 38 2020 Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294 Li, Xiaoli; Shen, Jie 38 2020 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 Remarks on the pressure error estimates for the projection methods. Zbl 0802.76060 Shen, Jie 36 1994 Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437 Cai, Jiaxiang; Shen, Jie 36 2020 A spectral-element method for transmission eigenvalue problems. Zbl 1292.65119 An, Jing; Shen, Jie 36 2013 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 35 2005 Mass and volume conservation in phase field models for binary fluids. Zbl 1373.76317 Shen, Jie; Yang, Xiaofeng; Wang, Qi 35 2013 Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075 Mao, Zhiping; Shen, Jie 35 2017 Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078 Liu, Fei; Shen, Jie 34 2015 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 numerical approximations of forward-backward stochastic differential equations. Zbl 1177.60064 Ma, Jin; Shen, Jie; Zhao, Yanhong 31 2008 Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007 Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie 31 2005 Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains. Zbl 1154.65082 Shen, Jie; Wang, Li-Lian 31 2007 On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0739.76017 Shen, Jie 30 1992 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 Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. Zbl 1215.65179 Shen, Jie; Wang, Li-Lian 27 2010 A triangular spectral element method using fully tensorial rational basis functions. Zbl 1197.65187 Shen, Jie; Wang, Li-Lian; Li, Huiyuan 27 2009 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 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 A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. Zbl 1123.76049 Fang, Qirong; Nicholls, David P.; Shen, Jie 24 2007 Generalized Laguerre approximation and its applications to exterior problems. Zbl 1073.65130 Guo, Benyu; Shen, Jie; Xu, Chenglong 24 2005 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 Global constraints preserving scalar auxiliary variable schemes for gradient flows. Zbl 1456.65087 Cheng, Qing; Shen, Jie 24 2020 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 24 2019 Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305 Mao, Zhiping; Shen, Jie 24 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 23 2018 An efficient spectral method for acoustic scattering from rough surfaces. Zbl 1164.65303 Xiu, Dongbin; 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 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 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 1 2023 A variable time-step IMEX-BDF2 SAV scheme and its sharp error estimate for the Navier-Stokes equations. Zbl 07737653 Di, Yana; Ma, Yuheng; Shen, Jie; Zhang, Jiwei 1 2023 A fictitious domain spectral method for solving the Helmholtz equation in exterior domains. Zbl 07698882 Gu, Yiqi; Shen, Jie 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 A new Lagrange multiplier approach for constructing structure preserving schemes. II: Bound preserving. Zbl 1491.65110 Cheng, Qing; Shen, Jie 9 2022 On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of two-phase incompressible flows. Zbl 07524187 Li, Xiaoli; Shen, Jie 8 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 Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation. Zbl 07595981 Li, Xiaoli; Shen, Jie 5 2022 Log orthogonal functions: approximation properties and applications. Zbl 1481.65037 Chen, Sheng; 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 18 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 12 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 8 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 49 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 41 2020 Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167 Li, Xiaoli; Shen, Jie 38 2020 Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294 Li, Xiaoli; Shen, Jie 38 2020 Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437 Cai, Jiaxiang; Shen, Jie 36 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 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 Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. Zbl 1440.65192 Chen, Hongtao; Mao, Jingjing; 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 20 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 8 2020 Bound preserving and energy dissipative schemes for porous medium equation. Zbl 1436.65101 Gu, Yiqi; Shen, Jie 5 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 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 287 2019 Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165 Li, Xiaoli; Shen, Jie; Rui, Hongxing 71 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 52 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 24 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 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 3 2019 Fundamental gaps of the fractional Schrödinger operator. Zbl 1429.35195 Bao, Weizhu; Ruan, Xinran; Shen, Jie; Sheng, Changtao 2 2019 The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181 Shen, Jie; Xu, Jie; Yang, Jiang 474 2018 Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047 Shen, Jie; Xu, Jie 177 2018 Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045 Cheng, Qing; Shen, Jie 69 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 Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305 Mao, Zhiping; Shen, Jie 24 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 23 2018 Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy. Zbl 1475.82027 Shen, Jie; Xu, Jie 15 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 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 10 2018 A tight bound of hard thresholding. Zbl 1473.62287 Shen, Jie; Li, Ping 8 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 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 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 141 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 35 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 17 2017 A hybrid spectral element method for fractional two-point boundary value problems. Zbl 1413.65307 Sheng, Changtao; Shen, Jie 14 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 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 The generation of symmetric and asymmetric lumps by a bottom topography. Zbl 1524.35539 Hu, Wencheng; Huang, Wenhua; Shen, Jie; Lu, Zhiming 1 2017 Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066 Chen, Sheng; Shen, Jie; Wang, Li-Lian 162 2016 On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059 Shen, Jie; Tang, Tao; Yang, Jiang 95 2016 Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229 Chen, Ying; Shen, Jie 75 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 72 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 61 2016 Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395 Mao, Zhiping; Shen, Jie 59 2016 Efficient splitting schemes for magneto-hydrodynamic equations. Zbl 1388.76224 Choi, Heejun; Shen, Jie 19 2016 Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. Zbl 1416.65482 Shen, Jie; Wang, Yingwei 19 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 12 2016 A hybrid spectral element method for Volterra integral equations with weakly singular kernel. Zbl 1499.65770 Sheng, Changtao; Shen, Jie 3 2016 Two-phase Stefan problem with smoothed enthalpy. Zbl 1349.35433 Azaïez, M.; Jelassi, F.; Brahim, M. Mint; Shen, J. 2 2016 ...and 150 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,342 Authors 124 Shen, Jie 118 Yang, Xiaofeng 59 Wang, Cheng 58 He, Yinnian 57 Guo, Ben-Yu 53 Kim, Junseok 53 Wang, Lilian 51 Feng, Xinlong 51 Wang, Yushun 47 Wang, Qi 45 Wang, Zhongqing 45 Zhao, Jia 44 Chen, Yanping 42 Wise, Steven M. 38 Zhang, Zhimin 37 Mei, Liquan 35 Gong, Yuezheng 35 Huang, Yunqing 34 Liu, Chun 33 Dehghan Takht Fooladi, Mehdi 33 Li, Huiyuan 33 Xu, Chuanju 30 Chen, Wenbin 30 Karniadakis, George Em 30 Wang, Hong 30 Zaky, Mahmoud A. 29 Ju, Lili 29 Qiao, Zhonghua 29 Zhang, Jun 28 Doha, Eid H. 28 Dong, Suchuan 28 Yang, Junxiang 27 Li, Xiaoli 27 Li, Yibao 26 Sun, Shuyu 25 Bao, Weizhu 25 Cai, Wenjun 25 Chen, Chuanjun 25 Tang, Tao 25 Wang, Tianjun 24 Du, Qiang 24 Hou, Yanren 24 Kou, Jisheng 23 Bhrawy, Ali Hassan 23 Han, Daozhi 23 Nicholls, David P. 23 Wang, Xiaoming 22 An, Jing 22 Guermond, Jean-Luc 22 He, Xiaoming 22 Jiang, Chaolong 22 Zheng, Xiangcheng 21 López, Juan Manuel 21 Qian, Xu 21 Song, Songhe 20 Lee, Hyun Geun 20 Li, Jian 20 Parand, Kourosh 19 Cai, Yongyong 19 Chen, Lizhen 19 Hendy, Ahmed S. 19 Jia, Hongen 19 Lin, Ping 19 Liu, Wen-Jie 19 Zhang, Tong 18 Guillén González, Francisco M. 18 Li, Buyang 18 Ma, Heping 18 Miranville, Alain M. 18 Wu, Boying 18 Zhang, Zhengru 17 Li, Dongfang 17 Liu, Zhengguang 17 Mao, Zhiping 17 Yang, Jiang 17 Yang, Yidu 17 Yi, Lijun 16 Jiang, Xiaoyun 16 Li, Xiao 16 Liu, Fawang 16 Su, Haiyan 16 Wu, Hao 16 Zhang, Hong 16 Zhang, Luming 16 Zhou, Jianwei 15 Hong, Qi 15 Hou, Dianming 15 Lowengrub, John Samuel 15 Marques, Francisco 15 Minev, Peter Dimitrov 15 Si, Zhiyong 15 Wang, Quan 15 Yang, Yin 14 Azaïez, Mejdi 14 Bi, Hai 14 Feng, James J. 14 Grasselli, Maurizio 14 Han, Jiayu 14 Huang, Pengzhan 14 Liao, HongLin ...and 5,242 more Authors all top 5 Cited in 344 Serials 613 Journal of Computational Physics 374 Journal of Scientific Computing 221 Applied Numerical Mathematics 196 Journal of Computational and Applied Mathematics 192 Computers & Mathematics with Applications 175 Computer Methods in Applied Mechanics and Engineering 120 Computers and Fluids 118 Applied Mathematics and Computation 116 SIAM Journal on Scientific Computing 105 Journal of Fluid Mechanics 96 SIAM Journal on Numerical Analysis 93 Numerical Methods for Partial Differential Equations 86 Numerical Algorithms 85 Communications in Computational Physics 74 International Journal of Computer Mathematics 72 Mathematics of Computation 71 Communications in Nonlinear Science and Numerical Simulation 68 Applied Mathematics Letters 67 Advances in Computational Mathematics 57 Mathematical Methods in the Applied Sciences 54 Computer Physics Communications 54 Discrete and Continuous Dynamical Systems. 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Real World Applications 8 International Journal of Computational Methods 8 International Journal of Applied and Computational Mathematics 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Journal of Approximation Theory 7 Acta Mathematica Scientia. Series B. (English Edition) 7 Multiscale Modeling & Simulation 7 Acta Numerica 7 Boundary Value Problems 7 S\(\vec{\text{e}}\)MA Journal 7 AIMS Mathematics 7 Electronic Research Archive 6 Journal of Inequalities and Applications 6 Networks and Heterogeneous Media 6 Mathematical Sciences 6 SIAM/ASA Journal on Uncertainty Quantification 5 International Journal of Engineering Science 5 Journal of Engineering Mathematics 5 Journal of Statistical Physics 5 Acta Applicandae Mathematicae 5 Acta Mathematicae Applicatae Sinica. 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