Edit Profile (opens in new tab) Shen, Jie Compute Distance To: Compute Author ID: shen.jie Published as: Shen, Jie; Shen, J. External Links: MGP Documents Indexed: 269 Publications since 1988, including 2 Books 5 Contributions as Editor Biographic References: 1 Publication Co-Authors: 111 Co-Authors with 194 Joint Publications 4,742 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 9 Li, Xiaoli 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 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 Wu, Ke 3 Yang, Jiang 2 Alici, Haydar 2 Azaïez, Mejdi 2 Cao, Duo 2 Chen, Hongtao 2 Chen, Ying 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 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 Goubet, Olivier 1 Gresho, Philip M. 1 Guo, Benqi 1 Guo, Zhichang ...and 76 more Co-Authors all top 5 Serials 41 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 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 Communications in Mathematical Sciences 5 Numerical Mathematics: Theory, Methods and Applications 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 Mathematical Biosciences and Engineering 2 Science China. Mathematics 2 Scientia Sinica. Mathematica 1 Applicable Analysis 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 International Journal of Theoretical Physics 1 Wave Motion 1 Fluid Dynamics Research 1 Indiana University Mathematics Journal 1 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 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 all top 5 Fields 208 Numerical analysis (65-XX) 130 Partial differential equations (35-XX) 105 Fluid mechanics (76-XX) 14 Approximations and expansions (41-XX) 13 Statistical mechanics, structure of matter (82-XX) 10 Optics, electromagnetic theory (78-XX) 8 Ordinary differential equations (34-XX) 7 Special functions (33-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Computer science (68-XX) 6 Real functions (26-XX) 6 Probability theory and stochastic processes (60-XX) 6 Biology and other natural sciences (92-XX) 5 Quantum theory (81-XX) 5 Geophysics (86-XX) 4 General and overarching topics; collections (00-XX) 4 Classical thermodynamics, heat transfer (80-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 Operations research, mathematical programming (90-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-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 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 232 Publications have been cited 8,183 times in 3,791 Documents Cited by ▼ Year ▼ An overview of projection methods for incompressible flows. Zbl 1122.76072Guermond, J. L.; Minev, P.; Shen, Jie 444 2006 Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Zbl 1201.65184Shen, Jie; Yang, Xiaofeng 388 2010 Spectral methods. Algorithms, analysis and applications. Zbl 1227.65117Shen, Jie; Tang, Tao; Wang, Li-Lian 372 2011 The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181Shen, Jie; Xu, Jie; Yang, Jiang 312 2018 Efficient spectral-Galerkin method. I: Direct solvers of second- and fourth-order equations using Legendre polynomials. Zbl 0811.65097Shen, Jie 293 1994 A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Zbl 1092.76069Liu, Chun; Shen, Jie 243 2003 A diffuse-interface method for simulating two-phase flows of complex fluids. Zbl 1130.76437Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie 239 2004 Spectral and high-order methods with applications. Zbl 1234.65005Shen, Jie; Tang, Tao 217 2006 Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: Application to thin film epitaxy. Zbl 1247.65088Shen, Jie; Wang, Cheng; Wang, Xiaoming; Wise, Steven M. 193 2012 A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080Shen, Jie; Xu, Jie; Yang, Jiang 166 2019 A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities. Zbl 1410.76464Shen, Jie; Yang, Xiaofeng 157 2010 Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066Chen, Sheng; Shen, Jie; Wang, Li-Lian 134 2016 On error estimates of projection methods for Navier-Stokes equations: First-order schemes. Zbl 0741.76051Shen, Jie 131 1992 Applications of semi-implicit Fourier-spectral method to phase field equations. Zbl 1017.65533Chen, L. Q.; Shen, Jie 125 1998 Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047Shen, Jie; Xu, Jie 123 2018 Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178Shen, Jie; Yang, Xiaofeng 120 2015 Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. Zbl 1158.76319Yang, Xiaofeng; Feng, James J.; Liu, Chun; Shen, Jie 114 2006 Efficient spectral-Galerkin method. II: Direct solvers of second- and fourth-order equations using Chebyshev polynomials. Zbl 0840.65113Shen, Jie 108 1995 On the error estimates for the rotational pressure-correction projection methods. Zbl 1093.76050Guermond, J. L.; Shen, Jie 107 2004 Numerical approximations for a three-component Cahn-Hilliard phase-field model based on the invariant energy quadratization method. Zbl 1393.80003Yang, Xiaofeng; Zhao, Jia; Wang, Qi; Shen, Jie 105 2017 On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes. Zbl 0855.76049Shen, Jie 104 1996 Velocity-correction projection methods for incompressible flows. Zbl 1130.76395Guermond, J. L.; Shen, Jie 101 2003 Stable and efficient spectral methods in unbounded domains using Laguerre functions. Zbl 0979.65105Shen, Jie 95 2000 Long time stability and convergence for fully discrete nonlinear Galerkin methods. Zbl 0684.65095Shen, Jie 94 1990 Optimal spectral-Galerkin methods using generalized Jacobi polynomials. Zbl 1102.76047Guo, Benyu; Shen, Jie; Wang, Li-Lian 86 2006 On error estimates of the penalty method for unsteady Navier-Stokes equations. Zbl 0822.35008Shen, Jie 83 1995 Some recent advances on spectral methods for unbounded domains. Zbl 1364.65265Shen, Jie; Wang, Li-Lian 76 2009 Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Zbl 0969.65094Guo, Ben-Yu; Shen, Jie 73 2000 Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Zbl 1400.65049Shen, Jie; Yang, Xiaofeng 72 2010 A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. Zbl 1277.76118Dong, S.; Shen, J. 71 2012 A new class of truly consistent splitting schemes for incompressible flows. Zbl 1032.76529Guermond, J. L.; Shen, Jie 71 2003 A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. Zbl 1084.35083Bao, Weizhu; Shen, Jie 68 2005 A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KdV equation. Zbl 1053.65085Shen, Jie 67 2003 On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059Shen, Jie; Tang, Tao; Yang, Jiang 66 2016 Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184Shen, Jie; Yang, Xiaofeng; Yu, Haijun 63 2015 Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations. Zbl 1382.65222Mao, Zhiping; Chen, Sheng; Shen, Jie 62 2016 Hopf bifurcation of the unsteady regularized driven cavity flow. Zbl 0725.76059Shen, Jie 59 1991 Efficient spectral-Galerkin methods. III: Polar and cylindrical geometries. Zbl 0890.65117Shen, Jie 55 1997 A rational approximation and its applications to differential equations on the half line. Zbl 0984.65104Guo, Benyu; Shen, Jie; Wang, Zhongqing 53 2000 Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. Zbl 1326.76064Liu, Chun; Shen, Jie; Yang, Xiaofeng 53 2015 Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1109.76037Pyo, Jae-Hong; Shen, Jie 52 2007 Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395Mao, Zhiping; Shen, Jie 51 2016 Generalized Jacobi polynomials/functions and their applications. Zbl 1171.33006Guo, Ben-Yu; Shen, Jie; Wang, Li-Lian 50 2009 A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids. Zbl 1349.76019Zhao, Jia; Yang, Xiaofeng; Shen, Jie; Wang, Qi 50 2016 Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229Chen, Ying; Shen, Jie 50 2016 Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045Cheng, Qing; Shen, Jie 50 2018 Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Zbl 1118.65111Shen, Jie; Wang, Li-Lian 49 2007 Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057Shen, Jie; Yang, Xiaofeng 48 2014 An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161Collins, Craig; Shen, Jie; Wise, Steven M. 48 2013 Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions. Zbl 1083.76044Guermond, J. L.; Minev, P.; Shen, J. 45 2005 An efficient moving mesh spectral method for the phase-field model of two-phase flows. Zbl 1159.76032Shen, Jie; Yang, Xiaofeng 44 2009 Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165Li, Xiaoli; Shen, Jie; Rui, Hongxing 43 2019 Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval. Zbl 1001.65129Guo, Benyu; Shen, Jie; Wang, Zhongqing 42 2002 Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems. Zbl 1388.65117Chen, Feng; Shen, Jie 42 2013 Efficient stochastic Galerkin methods for random diffusion equations. Zbl 1161.65008Xiu, Dongbin; Shen, Jie 41 2009 Spectral and pseudospectral approximations using Hermite functions: Application to the Dirac equation. Zbl 1032.33004Guo, Ben-yu; Shen, Jie; Xu, Cheng-long 40 2003 Efficient spectral sparse grid methods and applications to high-dimensional elliptic problems. Zbl 1233.65094Shen, Jie; Yu, Haijun 39 2010 On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0782.76025Shen, Jie 38 1992 Pressure boundary condition for the time-dependent incompressible Navier-Stokes equations. Zbl 1155.76322Sani, R. L.; Shen, J.; Pironneau, O.; Gresho, P. M. 36 2006 Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie 36 2005 Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach. Zbl 1444.76020Cheng, Qing; Shen, Jie; Yang, Xiaofeng 35 2019 An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. I: Axisymmetric cases. Zbl 0908.76068Lopez, J. M.; Shen, Jie 35 1998 A generalized-Laguerre-Fourier-Hermite pseudospectral method for computing the dynamics of rotating Bose-Einstein condensates. Zbl 1205.82096Bao, Weizhu; Li, Hailiang; Shen, Jie 34 2009 An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. Zbl 1181.76019Feng, James J.; Liu, Chun; Shen, Jie; Yue, Pengtao 34 2005 Remarks on the pressure error estimates for the projection methods. Zbl 0802.76060Shen, Jie 33 1994 On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line. Zbl 0992.65111Guo, Ben-Yu; Shen, Jie 32 2001 A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211Cheng, Qing; Liu, Chun; Shen, Jie 32 2020 Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. Zbl 1380.65203Cheng, Qing; Yang, Xiaofeng; Shen, Jie 32 2017 Spectral approximation of the Helmholtz equation with high wave numbers. Zbl 1091.65119Shen, Jie; Wang, Li-Lian 31 2005 Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains. Zbl 1154.65082Shen, Jie; Wang, Li-Lian 30 2007 A spectral-element method for transmission eigenvalue problems. Zbl 1292.65119An, Jing; Shen, Jie 30 2013 Mass and volume conservation in phase field models for binary fluids. Zbl 1373.76317Shen, Jie; Yang, Xiaofeng; Wang, Qi 30 2013 Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie 28 2005 On numerical approximations of forward-backward stochastic differential equations. Zbl 1177.60064Ma, Jin; Shen, Jie; Zhao, Yanhong 26 2008 Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. Zbl 1215.65179Shen, Jie; Wang, Li-Lian 26 2010 Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422Liu, Chun; Shen, Jie; Yang, Xiaofeng 26 2007 On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0739.76017Shen, Jie 25 1992 Generalized Laguerre approximation and its applications to exterior problems. Zbl 1073.65130Guo, Benyu; Shen, Jie; Xu, Chenglong 25 2005 Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. Zbl 1286.65112Yang, Xiaofeng; Forest, M. Gregory; Li, Huiyuan; Liu, Chun; Shen, Jie; Wang, Qi; Chen, Falai 24 2013 A triangular spectral element method using fully tensorial rational basis functions. Zbl 1197.65187Shen, Jie; Wang, Li-Lian; Li, Huiyuan 24 2009 A stable high-order method for two-dimensional bounded-obstacle scattering. Zbl 1130.78007Nicholls, David P.; Shen, Jie 24 2006 Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078Liu, Fei; Shen, Jie 24 2015 The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems. Zbl 1484.65196Shen, Jie; Yang, Xiaofeng 24 2020 A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. Zbl 1123.76049Fang, Qirong; Nicholls, David P.; Shen, Jie 23 2007 An efficient spectral method for acoustic scattering from rough surfaces. Zbl 1164.65303Xiu, Dongbin; Shen, Jie 22 2007 Mode interactions in an enclosed swirling flow: A double Hopf bifurcation between azimuthal wavenumbers 0 and 2. Zbl 1016.76029Marques, 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 1130.76392Lopez, J. M.; Marques, F.; Shen, Jie 22 2002 A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210Huang, Fukeng; Shen, Jie; Yang, Zhiguo 22 2020 Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167Li, Xiaoli; Shen, Jie 22 2020 Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437Cai, Jiaxiang; Shen, Jie 22 2020 Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle. Zbl 1197.65176Li, Huiyuan; Shen, Jie 20 2010 Instability and mode interactions in a differentially driven rotating cylinder. Zbl 1042.76026Lopez, J. M.; Hart, J. E.; Marques, F.; Kittelman, S.; Shen, J. 20 2002 Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075Mao, Zhiping; Shen, Jie 20 2017 Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Zbl 1382.35184Cai, Yongyong; Choi, Heejun; Shen, Jie 20 2017 Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven 20 2018 Legendre and Chebyshev dual-Petrov-Galerkin methods for hyperbolic equations. Zbl 1173.65342Shen, Jie; Wang, Li-Lian 18 2007 A dual-Petrov-Galerkin method for the Kawahara-type equations. Zbl 1133.76040Yuan, Juan-Ming; Shen, Jie; Wu, Jiahong 18 2008 On liquid crystal flows with free-slip boundary conditions. Zbl 1014.76005Liu, Chun; Shen, Jie 18 2001 Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305Mao, Zhiping; Shen, Jie 18 2018 Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294Li, Xiaoli; Shen, Jie 18 2020 New SAV-pressure correction methods for the Navier-Stokes equations: stability and error Analysis. Zbl 1479.35625Li, Xiaoli; Shen, Jie; Liu, Zhengguang 7 2022 A new Lagrange multiplier approach for constructing structure preserving schemes. I: Positivity preserving. Zbl 07487691Cheng, Qing; Shen, Jie 5 2022 A new class of implicit-explicit BDF\(k\) SAV schemes for general dissipative systems and their error analysis. Zbl 07526020Huang, Fukeng; Shen, Jie 4 2022 A generalized SAV approach with relaxation for dissipative systems. Zbl 07540356Zhang, Yanrong; Shen, Jie 4 2022 A new class of higher-order decoupled schemes for the incompressible Navier-Stokes equations and applications to rotating dynamics. Zbl 07527723Wu, Ke; Huang, Fukeng; Shen, Jie 3 2022 Discrete maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation. Zbl 1489.65124Shen, Jie; Zhang, Xiangxiong 3 2022 A new Lagrange multiplier approach for constructing structure preserving schemes. II: Bound preserving. Zbl 1491.65110Cheng, Qing; Shen, Jie 2 2022 Log orthogonal functions: approximation properties and applications. Zbl 1481.65037Chen, Sheng; Shen, Jie 1 2022 Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system. Zbl 1485.65102Chen, Wenbin; Liu, Qianqian; Shen, Jie 1 2022 Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations. Zbl 07525157Huang, Fukeng; Shen, Jie; Wu, Ke 1 2022 Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations. Zbl 1491.65086Shen, Jie; Xu, Jie 7 2021 Generalized SAV approaches for gradient systems. Zbl 1475.65066Cheng, Qing; Liu, Chun; Shen, Jie 7 2021 Bound/positivity preserving and energy stable scalar auxiliary variable schemes for dissipative systems: applications to Keller-Segel and Poisson-Nernst-Planck equations. Zbl 07364339Huang, Fukeng; Shen, Jie 7 2021 Stability and error analysis of a class of high-order IMEX schemes for Navier-Stokes equations with periodic boundary conditions. Zbl 1496.65180Huang, Fukeng; Shen, Jie 5 2021 Scalar auxiliary variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 07505911Antoine, Xavier; Shen, Jie; Tang, Qinglin 3 2021 A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations. Zbl 07508502Li, Maojun; Cheng, Yongping; Shen, Jie; Zhang, Xiangxiong 2 2021 Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis. Zbl 1491.65111Deng, Beichuan; Shen, Jie; Zhuang, Qingqu 1 2021 Efficient and accurate SAV schemes for the generalized Zakharov systems. Zbl 1465.35362Shen, Jie; Zheng, Nan 1 2021 Computing interface with quasiperiodicity. Zbl 07508468Cao, Duo; Shen, Jie; Xu, Jie 1 2021 A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211Cheng, Qing; Liu, Chun; Shen, Jie 32 2020 The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems. Zbl 1484.65196Shen, Jie; Yang, Xiaofeng 24 2020 A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210Huang, Fukeng; Shen, Jie; Yang, Zhiguo 22 2020 Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167Li, Xiaoli; Shen, Jie 22 2020 Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437Cai, Jiaxiang; Shen, Jie 22 2020 Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294Li, Xiaoli; Shen, Jie 18 2020 Fast Fourier-like mapped Chebyshev spectral-Galerkin methods for PDEs with integral fractional Laplacian in unbounded domains. Zbl 1450.65154Sheng, Changtao; Shen, Jie; Tang, Tao; Wang, Li-Lian; Yuan, Huifang 16 2020 Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. Zbl 1440.65192Chen, Hongtao; Mao, Jingjing; Shen, Jie 12 2020 A spectrally accurate approximation to subdiffusion equations using the log orthogonal functions. Zbl 1434.65291Chen, Sheng; Shen, Jie; Zhang, Zhimin; Zhou, Zhi 11 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 1471.65106Li, Xiaoli; Shen, Jie 11 2020 Global constraints preserving scalar auxiliary variable schemes for gradient flows. Zbl 1456.65087Cheng, Qing; Shen, Jie 9 2020 Unconditionally bound preserving and energy dissipative schemes for a class of Keller-Segel equations. Zbl 1440.65101Shen, Jie; Xu, Jie 8 2020 Bound preserving and energy dissipative schemes for porous medium equation. Zbl 1436.65101Gu, Yiqi; Shen, Jie 3 2020 Error estimate of Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1427.76124Chen, Hongtao; Mao, Jingjing; Shen, Jie 2 2020 An efficient and accurate numerical method for the spectral fractional Laplacian equation. Zbl 1433.65235Chen, Sheng; Shen, Jie 2 2020 Accurate and efficient spectral methods for elliptic PDEs in complex domains. Zbl 1440.65160Gu, Yiqi; Shen, Jie 2 2020 A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions. Zbl 1446.65128Hu, Jingwei; Shen, Jie; Wang, Yingwei 2 2020 A total fractional-order variation model for image super-resolution and its SAV algorithm. Zbl 1439.65100Yao, 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 1422.65080Shen, Jie; Xu, Jie; Yang, Jiang 166 2019 Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165Li, Xiaoli; Shen, Jie; Rui, Hongxing 43 2019 Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach. Zbl 1444.76020Cheng, 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 1452.65116Zhuang, Qingqu; Shen, Jie 12 2019 An efficient space-time method for time fractional diffusion equation. Zbl 1466.65214Shen, Jie; Sheng, Chang-Tao 8 2019 Stability and convergence analysis of rotational velocity correction methods for the Navier-Stokes equations. Zbl 1435.65119Chen, Feng; Shen, Jie 6 2019 Efficient and accurate structure preserving schemes for complex nonlinear systems. Zbl 1446.65213Shen, Jie 5 2019 Distributional compatibility for change of measures. Zbl 1420.60027Shen, Jie; Shen, Yi; Wang, Bin; Wang, Ruodu 4 2019 Fundamental gaps of the fractional Schrödinger operator. Zbl 1429.35195Bao, Weizhu; Ruan, Xinran; Shen, Jie; Sheng, Changtao 1 2019 Fast structured Jacobi-Jacobi transforms. Zbl 07040627Shen, Jie; Wang, Yingwei; Xia, Jianlin 1 2019 The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181Shen, Jie; Xu, Jie; Yang, Jiang 312 2018 Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047Shen, Jie; Xu, Jie 123 2018 Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045Cheng, Qing; Shen, Jie 50 2018 Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven 20 2018 Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305Mao, 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 1390.35225Cai, Yongyong; Shen, Jie 12 2018 Laguerre functions and their applications to tempered fractional differential equations on infinite intervals. Zbl 1398.65314Chen, Sheng; Shen, Jie; Wang, Li-Lian 12 2018 Enriched spectral methods and applications to problems with weakly singular solutions. Zbl 1406.65123Chen, Sheng; Shen, Jie 9 2018 A space-time Petrov-Galerkin spectral method for time fractional diffusion equation. Zbl 1438.65308Sheng, Changtao; Shen, Jie 7 2018 Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy. Zbl 1475.82027Shen, Jie; Xu, Jie 3 2018 A tight bound of hard thresholding. Zbl 1473.62287Shen, Jie; Li, Ping 3 2018 Wavenumber explicit analysis for time-harmonic Maxwell equations in a spherical shell and spectral approximations. Zbl 1477.78001Ma, 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 1424.65119Alici, Haydar; Shen, Jie 2 2018 Preconditioning techniques in Chebyshev collocation method for elliptic equations. Zbl 1408.35025Fang, Zhi-Wei; Shen, Jie; Sun, Hai-Wei 1 2018 Approximations on \(\mathrm{SO}(3)\) by Wigner D-matrix and applications. Zbl 1398.65321Shen, Jie; Xu, Jie; Zhang, Pingwen 1 2018 Numerical approximations for a three-component Cahn-Hilliard phase-field model based on the invariant energy quadratization method. Zbl 1393.80003Yang, Xiaofeng; Zhao, Jia; Wang, Qi; Shen, Jie 105 2017 Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. Zbl 1380.65203Cheng, Qing; Yang, Xiaofeng; Shen, Jie 32 2017 Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075Mao, Zhiping; Shen, Jie 20 2017 Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Zbl 1382.35184Cai, Yongyong; Choi, Heejun; Shen, Jie 20 2017 A hybrid spectral element method for fractional two-point boundary value problems. Zbl 1413.65307Sheng, Changtao; Shen, Jie 12 2017 Unconditionally stable Gauge-Uzawa finite element schemes for incompressible natural convection problems with variable density. Zbl 1380.76132Wu, Jilian; Shen, Jie; Feng, Xinlong 10 2017 A stable scheme and its convergence analysis for a 2D dynamic \(Q\)-tensor model of nematic liquid crystals. Zbl 1368.76048Cai, Yongyong; Shen, Jie; Xu, Xiang 6 2017 A nodal sparse grid spectral element method for multi-dimensional elliptic partial differential equations. Zbl 1429.65287Rong, Zhijian; Shen, Jie; Yu, Haijun 2 2017 Online optimization for max-norm regularization. Zbl 1454.68132Shen, Jie; Xu, Huan; Li, Ping 2 2017 Numerical analysis and simulation for a generalized planar Ginzburg-Landau equation in a circular geometry. Zbl 1367.65142Colbert-Kelly, Sean; McFadden, Geoffrey B.; Phillips, Daniel; Shen, Jie 1 2017 Highly accurate pseudospectral approximations of the prolate spheroidal wave equation for any bandwidth parameter and zonal wavenumber. Zbl 1416.65224Alıcı, H.; Shen, Jie 1 2017 Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066Chen, Sheng; Shen, Jie; Wang, Li-Lian 134 2016 On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059Shen, Jie; Tang, Tao; Yang, Jiang 66 2016 Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations. Zbl 1382.65222Mao, Zhiping; Chen, Sheng; Shen, Jie 62 2016 Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395Mao, Zhiping; Shen, Jie 51 2016 A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids. Zbl 1349.76019Zhao, Jia; Yang, Xiaofeng; Shen, Jie; Wang, Qi 50 2016 Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229Chen, Ying; Shen, Jie 50 2016 Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. Zbl 1416.65482Shen, Jie; Wang, Yingwei 16 2016 Fast structured direct spectral methods for differential equations with variable coefficients. I. The one-dimensional case. Zbl 1330.65124Shen, Jie; Wang, Yingwei; Xia, Jianlin 11 2016 Efficient splitting schemes for magneto-hydrodynamic equations. Zbl 1388.76224Choi, Heejun; Shen, Jie 11 2016 Two-phase Stefan problem with smoothed enthalpy. Zbl 1349.35433Azaïez, M.; Jelassi, F.; Brahim, M. Mint; Shen, J. 2 2016 Efficient spectral-Galerkin method and analysis for elliptic PDEs with non-local boundary conditions. Zbl 1375.65159Hu, Lina; Ma, Lina; Shen, Jie 1 2016 Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178Shen, Jie; Yang, Xiaofeng 120 2015 Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184Shen, 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 1326.76064Liu, Chun; Shen, Jie; Yang, Xiaofeng 53 2015 Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078Liu, Fei; Shen, Jie 24 2015 Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. Zbl 1349.65721Shen, Jie; Sheng, Changtao; Wang, Zhongqing 17 2015 A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows. Zbl 1349.76198Dong, S.; Shen, J. 16 2015 Dynamic transitions of quasi-geostrophic channel flow. Zbl 1329.35232Dijkstra, 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 1333.76036Sengul, Taylan; Shen, Jie; Wang, Shouhong 11 2015 Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem. Zbl 1443.65306An, Jing; Shen, Jie 6 2015 Accurate solution and approximations of the linearized BGK equation for steady Couette flow. Zbl 1410.76412Li, Wei; Luo, Li-Shi; Shen, Jie 5 2015 Spectral approximation of time-harmonic Maxwell equations in three-dimensional exterior domains. Zbl 1329.65286Ma, Lina; Shen, Jie; Wang, Li-Lian 3 2015 Modeling and simulation of fingering pattern formation in a combustion model. Zbl 1318.80002Hu, 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 1488.65513Mao, Zhiping; Shen, Jie 1 2015 Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057Shen, Jie; Yang, Xiaofeng 48 2014 Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains. Zbl 1293.65161Shen, Jie; Wang, Li-Lian; Yu, Haijun 11 2014 A new spectral method for numerical solution of the unbounded rough surface scattering problem. Zbl 1349.65646He, Ying; Li, Peijun; Shen, Jie 7 2014 ...and 132 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,436 Authors 115 Shen, Jie 97 Yang, Xiaofeng 57 Guo, Ben-Yu 54 He, Yinnian 52 Wang, Cheng 45 Kim, Junseok 45 Wang, Zhongqing 44 Wang, Lilian 41 Wang, Qi 37 Feng, Xinlong 37 Zhao, Jia 35 Wang, Yushun 34 Wise, Steven M. 31 Chen, Yanping 31 Liu, Chun 30 Dehghan Takht Fooladi, Mehdi 29 Li, Huiyuan 29 Mei, Liquan 28 Zhang, Zhimin 27 Karniadakis, George Em 27 Xu, Chuanju 25 Doha, Eid H. 25 Gong, Yuezheng 25 Huang, Yunqing 25 Wang, Hong 24 Chen, Wenbin 23 Bhrawy, Ali Hassan 23 Tang, Tao 23 Zhang, Jun 22 Li, Xiaoli 22 Li, Yibao 22 Nicholls, David P. 21 Bao, Weizhu 21 Chen, Chuanjun 21 Du, Qiang 21 Guermond, Jean-Luc 21 Ju, Lili 21 Qiao, Zhonghua 21 Wang, Tianjun 21 Wang, Xiaoming 21 Zaky, Mahmoud A. 20 Han, Daozhi 20 Hou, Yanren 20 Lee, Hyun Geun 20 López, Juan Manuel 20 Sun, Shuyu 19 Yang, Junxiang 18 Cai, Yongyong 18 Kou, Jisheng 18 Miranville, Alain M. 17 Cai, Wenjun 17 He, Xiaoming 17 Li, Jian 17 Ma, Heping 17 Parand, Kourosh 16 Chen, Lizhen 16 Dong, Suchuan 16 Li, Buyang 16 Wu, Boying 15 Jiang, Chaolong 15 Lin, Ping 15 Liu, Wen-Jie 15 Marques, Francisco 15 Minev, Peter Dimitrov 15 Sherwin, Spencer J. 15 Wu, Hao 15 Yang, Jiang 14 An, Jing 14 Guillén González, Francisco M. 14 Lowengrub, John Samuel 14 Mao, Zhiping 14 Wang, Quan 14 Yi, Lijun 14 Zhang, Hui 13 Auteri, Franco 13 Codina, Ramon 13 Feng, James J. 13 Jia, Hongen 13 Li, Peijun 13 Liu, Zhengguang 13 Yu, Haijun 13 Zhang, Luming 13 Zheng, Xiangcheng 12 Abd-Elhameed, Waleed Mohamed 12 An, Rong 12 Hendy, Ahmed S. 12 Li, Dongfang 12 Li, Xiao 12 Liao, HongLin 12 Liu, Fawang 12 Liu, Hailiang 12 Lu, Shujuan 12 Si, Zhiyong 12 Tachim Medjo, Theodore 12 Wang, Kun 12 Yang, Yidu 12 Yue, Pengtao 12 Zhang, Zhengru 12 Zhou, Jianwei 11 Azaïez, Mejdi ...and 4,336 more Authors all top 5 Cited in 316 Serials 533 Journal of Computational Physics 308 Journal of Scientific Computing 186 Applied Numerical Mathematics 166 Journal of Computational and Applied Mathematics 147 Computer Methods in Applied Mechanics and Engineering 132 Computers & Mathematics with Applications 114 Computers and Fluids 101 Applied Mathematics and Computation 99 SIAM Journal on Scientific Computing 94 Journal of Fluid Mechanics 74 Communications in Computational Physics 72 SIAM Journal on Numerical Analysis 68 Mathematics of Computation 63 Numerical Algorithms 57 Advances in Computational Mathematics 56 International Journal of Computer Mathematics 51 Applied Mathematics Letters 46 Numerische Mathematik 42 Communications in Nonlinear Science and Numerical Simulation 42 Discrete and Continuous Dynamical Systems. Series B 38 Mathematical Methods in the Applied Sciences 36 Computational and Applied Mathematics 35 Numerical Methods for Partial Differential Equations 35 Physics of Fluids 31 Journal of Mathematical Analysis and Applications 30 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 30 Advances in Applied Mathematics and Mechanics 28 Applied Mathematical Modelling 26 International Journal for Numerical Methods in Fluids 25 Mathematics and Computers in Simulation 22 Science China. Mathematics 20 Advances in Difference Equations 19 Physica D 19 Mathematical Problems in Engineering 18 Computer Physics Communications 17 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 17 Discrete and Continuous Dynamical Systems. Series S 17 Communications on Applied Mathematics and Computation 16 East Asian Journal on Applied Mathematics 15 Journal of Differential Equations 15 International Journal of Numerical Analysis and Modeling 14 Calcolo 14 Abstract and Applied Analysis 13 BIT 13 SIAM Journal on Applied Mathematics 13 Computational Methods in Applied Mathematics 12 Journal of Applied Mathematics and Computing 11 Engineering Analysis with Boundary Elements 11 European Journal of Mechanics. B. Fluids 10 Applicable Analysis 10 Chaos, Solitons and Fractals 10 Numerical Functional Analysis and Optimization 10 International Journal of Computational Fluid Dynamics 10 Nonlinear Dynamics 10 Fractional Calculus & Applied Analysis 10 Journal of Mathematical Fluid Mechanics 10 Journal of Applied Mathematics 10 Frontiers of Mathematics in China 9 Archive for Rational Mechanics and Analysis 9 International Journal for Numerical Methods in Engineering 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Applied Mathematics and Mechanics. (English Edition) 9 Computational Mechanics 9 Journal of Non-Newtonian Fluid Mechanics 9 International Journal of Numerical Methods for Heat & Fluid Flow 9 Discrete and Continuous Dynamical Systems 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Communications on Pure and Applied Analysis 8 Chinese Annals of Mathematics. Series B 8 Nonlinear Analysis. Real World Applications 8 International Journal of Applied and Computational Mathematics 7 Acta Mechanica 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 SIAM Journal on Mathematical Analysis 7 Mathematical Modelling and Analysis 7 International Journal of Computational Methods 7 Boundary Value Problems 7 S\(\vec{\text{e}}\)MA Journal 7 AIMS Mathematics 6 Journal of Inequalities and Applications 6 International Journal of Nonlinear Sciences and Numerical Simulation 6 Multiscale Modeling & Simulation 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 ...and 216 more Serials all top 5 Cited in 50 Fields 2,792 Numerical analysis (65-XX) 1,709 Partial differential equations (35-XX) 1,567 Fluid mechanics (76-XX) 205 Mechanics of deformable solids (74-XX) 201 Ordinary differential equations (34-XX) 198 Statistical mechanics, structure of matter (82-XX) 140 Approximations and expansions (41-XX) 139 Integral equations (45-XX) 136 Real functions (26-XX) 101 Special functions (33-XX) 101 Biology and other natural sciences (92-XX) 95 Calculus of variations and optimal control; optimization (49-XX) 87 Optics, electromagnetic theory (78-XX) 85 Dynamical systems and ergodic theory (37-XX) 71 Probability theory and stochastic processes (60-XX) 71 Classical thermodynamics, heat transfer (80-XX) 57 Quantum theory (81-XX) 45 Geophysics (86-XX) 42 Harmonic analysis on Euclidean spaces (42-XX) 31 Computer science (68-XX) 29 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 26 Operator theory (47-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 24 Systems theory; control (93-XX) 14 Operations research, mathematical programming (90-XX) 12 Functional analysis (46-XX) 12 Mechanics of particles and systems (70-XX) 11 Statistics (62-XX) 11 Astronomy and astrophysics (85-XX) 10 Potential theory (31-XX) 10 Information and communication theory, circuits (94-XX) 6 Difference and functional equations (39-XX) 5 Integral transforms, operational calculus (44-XX) 4 Functions of a complex variable (30-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Relativity and gravitational theory (83-XX) 3 Number theory (11-XX) 3 Differential geometry (53-XX) 2 History and biography (01-XX) 2 Mathematical logic and foundations (03-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Topological groups, Lie groups (22-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 General topology (54-XX) Citations by Year