## Shen, Jie

Compute Distance To:
 Author ID: shen.jie Published as: Shen, Jie; Shen, J. External Links: MGP
 Documents Indexed: 265 Publications since 1988, including 2 Books 5 Contributions as Editor Biographic References: 1 Publication Co-Authors: 108 Co-Authors with 192 Joint Publications 4,313 Co-Co-Authors
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### Co-Authors

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

 40 Journal of Computational Physics 27 SIAM Journal on Numerical Analysis 23 Journal of Scientific Computing 21 SIAM Journal on Scientific Computing 10 Mathematics of Computation 9 Applied Numerical Mathematics 9 Communications in Computational Physics 7 Computer Methods in Applied Mechanics and Engineering 7 Numerische Mathematik 5 Journal of Fluid Mechanics 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Advances in Computational Mathematics 5 Discrete and Continuous Dynamical Systems 5 Communications in Mathematical Sciences 5 Numerical Mathematics: Theory, Methods and Applications 4 Journal of Computational and Applied Mathematics 4 Discrete and Continuous Dynamical Systems. Series B 4 International Journal of Numerical Analysis and Modeling 3 Mathematical Methods in the Applied Sciences 3 Physica D 3 Mathematical Problems in Engineering 3 Journal of Mathematical Study 3 East Asian Journal on Applied Mathematics 2 IMA Journal of Numerical Analysis 2 International Journal for Numerical Methods in Fluids 2 Chinese Annals of Mathematics. Series B 2 Journal of Computational Mathematics 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Applied Mathematics Letters 2 Machine Learning 2 Journal of Non-Newtonian Fluid Mechanics 2 Physics of Fluids 2 Journal of Liaoning Normal University. Natural Science Edition 2 Scientia Sinica. Mathematica 1 Applicable Analysis 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 International Journal of Theoretical Physics 1 Physics Letters. A 1 Wave Motion 1 Fluid Dynamics Research 1 Indiana University Mathematics Journal 1 International Journal for Numerical Methods in Engineering 1 Numerical Functional Analysis and Optimization 1 Acta Applicandae Mathematicae 1 Journal of Statistical Computation and Simulation 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Stochastic Processes and their Applications 1 Matemática Aplicada e Computacional 1 Advances in Differential Equations 1 Finance and Stochastics 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 IEEE Transactions on Image Processing 1 Foundations of Computational Mathematics 1 Journal of Machine Learning Research (JMLR) 1 Multiscale Modeling & Simulation 1 Mathematical Biosciences and Engineering 1 Springer Series in Computational Mathematics 1 Computational & Mathematical Methods in Medicine 1 Kinetic and Related Models 1 Science China. Mathematics 1 Mathematics Monograph Series 1 Communications on Applied Mathematics and Computation
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### Fields

 205 Numerical analysis (65-XX) 128 Partial differential equations (35-XX) 103 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 Quantum theory (81-XX) 5 Geophysics (86-XX) 5 Biology and other natural sciences (92-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) 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) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

230 Publications have been cited 7,965 times in 3,625 Documents Cited by Year
An overview of projection methods for incompressible flows. Zbl 1122.76072
Guermond, J. L.; Minev, P.; Shen, Jie
2006
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Zbl 1201.65184
Shen, Jie; Yang, Xiaofeng
2010
Spectral methods. Algorithms, analysis and applications. Zbl 1227.65117
Shen, Jie; Tang, Tao; Wang, Li-Lian
2011
The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181
Shen, Jie; Xu, Jie; Yang, Jiang
2018
Efficient spectral-Galerkin method. I: Direct solvers of second- and fourth-order equations using Legendre polynomials. Zbl 0811.65097
Shen, Jie
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
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
2004
Spectral and high-order methods with applications. Zbl 1234.65005
Shen, Jie; Tang, Tao
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.
2012
A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080
Shen, Jie; Xu, Jie; Yang, Jiang
2019
A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities. Zbl 1410.76464
Shen, Jie; Yang, Xiaofeng
2010
Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066
Chen, Sheng; Shen, Jie; Wang, Li-Lian
2016
On error estimates of projection methods for Navier-Stokes equations: First-order schemes. Zbl 0741.76051
Shen, Jie
1992
Applications of semi-implicit Fourier-spectral method to phase field equations. Zbl 1017.65533
Chen, L. Q.; Shen, Jie
1998
Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178
Shen, Jie; Yang, Xiaofeng
2015
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047
Shen, Jie; Xu, Jie
2018
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. Zbl 1158.76319
Yang, Xiaofeng; Feng, James J.; Liu, Chun; Shen, Jie
2006
Efficient spectral-Galerkin method. II: Direct solvers of second- and fourth-order equations using Chebyshev polynomials. Zbl 0840.65113
Shen, Jie
1995
On the error estimates for the rotational pressure-correction projection methods. Zbl 1093.76050
Guermond, J. L.; Shen, Jie
2004
On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes. Zbl 0855.76049
Shen, Jie
1996
Numerical approximations for a three-component Cahn-Hilliard phase-field model based on the invariant energy quadratization method. Zbl 1393.80003
Yang, Xiaofeng; Zhao, Jia; Wang, Qi; Shen, Jie
2017
Velocity-correction projection methods for incompressible flows. Zbl 1130.76395
Guermond, J. L.; Shen, Jie
2003
Stable and efficient spectral methods in unbounded domains using Laguerre functions. Zbl 0979.65105
Shen, Jie
2000
Long time stability and convergence for fully discrete nonlinear Galerkin methods. Zbl 0684.65095
Shen, Jie
1990
Optimal spectral-Galerkin methods using generalized Jacobi polynomials. Zbl 1102.76047
Guo, Benyu; Shen, Jie; Wang, Li-Lian
2006
On error estimates of the penalty method for unsteady Navier-Stokes equations. Zbl 0822.35008
Shen, Jie
1995
Some recent advances on spectral methods for unbounded domains. Zbl 1364.65265
Shen, Jie; Wang, Li-Lian
2009
Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Zbl 0969.65094
Guo, Ben-Yu; Shen, Jie
2000
Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Zbl 1400.65049
Shen, Jie; Yang, Xiaofeng
2010
A new class of truly consistent splitting schemes for incompressible flows. Zbl 1032.76529
Guermond, J. L.; Shen, Jie
2003
A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. Zbl 1277.76118
Dong, S.; Shen, J.
2012
A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. Zbl 1084.35083
Bao, Weizhu; Shen, Jie
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
2003
Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184
Shen, Jie; Yang, Xiaofeng; Yu, Haijun
2015
On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059
Shen, Jie; Tang, Tao; Yang, Jiang
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
2016
Hopf bifurcation of the unsteady regularized driven cavity flow. Zbl 0725.76059
Shen, Jie
1991
Efficient spectral-Galerkin methods. III: Polar and cylindrical geometries. Zbl 0890.65117
Shen, Jie
1997
A rational approximation and its applications to differential equations on the half line. Zbl 0984.65104
Guo, Benyu; Shen, Jie; Wang, Zhongqing
2000
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395
Mao, Zhiping; Shen, Jie
2016
Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. Zbl 1326.76064
Liu, Chun; Shen, Jie; Yang, Xiaofeng
2015
Generalized Jacobi polynomials/functions and their applications. Zbl 1171.33006
Guo, Ben-Yu; Shen, Jie; Wang, Li-Lian
2009
A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids. Zbl 1349.76019
Zhao, Jia; Yang, Xiaofeng; Shen, Jie; Wang, Qi
2016
An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161
Collins, Craig; Shen, Jie; Wise, Steven M.
2013
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045
Cheng, Qing; Shen, Jie
2018
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229
Chen, Ying; Shen, Jie
2016
Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1109.76037
Pyo, Jae-Hong; Shen, Jie
2007
Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Zbl 1118.65111
Shen, Jie; Wang, Li-Lian
2007
Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057
Shen, Jie; Yang, Xiaofeng
2014
Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions. Zbl 1083.76044
Guermond, J. L.; Minev, P.; Shen, J.
2005
An efficient moving mesh spectral method for the phase-field model of two-phase flows. Zbl 1159.76032
Shen, Jie; Yang, Xiaofeng
2009
Spectral and pseudospectral approximations using Hermite functions: Application to the Dirac equation. Zbl 1032.33004
Guo, Ben-yu; Shen, Jie; Xu, Cheng-long
2003
Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems. Zbl 1388.65117
Chen, Feng; Shen, Jie
2013
Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval. Zbl 1001.65129
Guo, Benyu; Shen, Jie; Wang, Zhongqing
2002
Efficient spectral sparse grid methods and applications to high-dimensional elliptic problems. Zbl 1233.65094
Shen, Jie; Yu, Haijun
2010
Efficient stochastic Galerkin methods for random diffusion equations. Zbl 1161.65008
Xiu, Dongbin; Shen, Jie
2009
Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165
Li, Xiaoli; Shen, Jie; Rui, Hongxing
2019
On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0782.76025
Shen, Jie
1992
An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. I: Axisymmetric cases. Zbl 0908.76068
Lopez, J. M.; Shen, Jie
1998
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Zbl 1195.76120
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2005
Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach. Zbl 1444.76020
Cheng, Qing; Shen, Jie; Yang, Xiaofeng
2019
An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. Zbl 1181.76019
Feng, James J.; Liu, Chun; Shen, Jie; Yue, Pengtao
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
2009
Pressure boundary condition for the time-dependent incompressible Navier-Stokes equations. Zbl 1155.76322
Sani, R. L.; Shen, J.; Pironneau, O.; Gresho, P. M.
2006
Remarks on the pressure error estimates for the projection methods. Zbl 0802.76060
Shen, Jie
1994
Spectral approximation of the Helmholtz equation with high wave numbers. Zbl 1091.65119
Shen, Jie; Wang, Li-Lian
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
2001
Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains. Zbl 1154.65082
Shen, Jie; Wang, Li-Lian
2007
Mass and volume conservation in phase field models for binary fluids. Zbl 1373.76317
Shen, Jie; Yang, Xiaofeng; Wang, Qi
2013
A spectral-element method for transmission eigenvalue problems. Zbl 1292.65119
An, Jing; Shen, Jie
2013
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
2020
Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. Zbl 1380.65203
Cheng, Qing; Yang, Xiaofeng; Shen, Jie
2017
Viscoelastic effects on drop deformation in steady shear. Zbl 1082.76007
Yue, Pengtao; Feng, James J.; Liu, Chun; Shen, Jie
2005
On numerical approximations of forward-backward stochastic differential equations. Zbl 1177.60064
Ma, Jin; Shen, Jie; Zhao, Yanhong
2008
Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. Zbl 1215.65179
Shen, Jie; Wang, Li-Lian
2010
On error estimates of some higher order penalty-projection methods for Navier-Stokes equations. Zbl 0739.76017
Shen, Jie
1992
A stable high-order method for two-dimensional bounded-obstacle scattering. Zbl 1130.78007
Nicholls, David P.; Shen, Jie
2006
Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. Zbl 1286.65112
Yang, Xiaofeng; Forest, M. Gregory; Li, Huiyuan; Liu, Chun; Shen, Jie; Wang, Qi; Chen, Falai
2013
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078
Liu, Fei; Shen, Jie
2015
Generalized Laguerre approximation and its applications to exterior problems. Zbl 1073.65130
Guo, Benyu; Shen, Jie; Xu, Chenglong
2005
A triangular spectral element method using fully tensorial rational basis functions. Zbl 1197.65187
Shen, Jie; Wang, Li-Lian; Li, Huiyuan
2009
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. Zbl 1123.76049
Fang, Qirong; Nicholls, David P.; Shen, Jie
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
2002
An efficient spectral method for acoustic scattering from rough surfaces. Zbl 1164.65303
Xiu, Dongbin; Shen, Jie
2007
Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422
Liu, Chun; Shen, Jie; Yang, Xiaofeng
2007
Mode interactions in an enclosed swirling flow: A double Hopf bifurcation between azimuthal wavenumbers 0 and 2. Zbl 1016.76029
Marques, F.; Lopez, J. M.; Shen, J.
2002
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437
Cai, Jiaxiang; Shen, Jie
2020
Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle. Zbl 1197.65176
Li, Huiyuan; Shen, Jie
2010
Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075
Mao, Zhiping; Shen, Jie
2017
Instability and mode interactions in a differentially driven rotating cylinder. Zbl 1042.76026
Lopez, J. M.; Hart, J. E.; Marques, F.; Kittelman, S.; Shen, J.
2002
Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014
Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven
2018
A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210
Huang, Fukeng; Shen, Jie; Yang, Zhiguo
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
2020
Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305
Mao, Zhiping; Shen, Jie
2018
Legendre and Chebyshev dual-Petrov-Galerkin methods for hyperbolic equations. Zbl 1173.65342
Shen, Jie; Wang, Li-Lian
2007
On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval. Zbl 1157.35093
Goubet, Olivier; Shen, Jie
2007
On liquid crystal flows with free-slip boundary conditions. Zbl 1014.76005
Liu, Chun; Shen, Jie
2001
An unconditionally stable rotational velocity-correction scheme for incompressible flows. Zbl 1425.76058
Dong, S.; Shen, J.
2010
Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. Zbl 1349.65721
Shen, Jie; Sheng, Changtao; Wang, Zhongqing
2015
Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. Zbl 1382.35184
Cai, Yongyong; Choi, Heejun; Shen, Jie
2017
New SAV-pressure correction methods for the Navier-Stokes equations: stability and error Analysis. Zbl 1479.35625
Li, Xiaoli; Shen, Jie; Liu, Zhengguang
2022
A new Lagrange multiplier approach for constructing structure preserving schemes. I: Positivity preserving. Zbl 07487691
Cheng, Qing; Shen, Jie
2022
Log orthogonal functions: approximation properties and applications. Zbl 1481.65037
Chen, Sheng; Shen, Jie
2022
Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations. Zbl 07525157
Huang, Fukeng; Shen, Jie; Wu, Ke
2022
A new class of implicit-explicit BDF$$k$$ SAV schemes for general dissipative systems and their error analysis. Zbl 07526020
Huang, Fukeng; Shen, Jie
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
2022
A generalized SAV approach with relaxation for dissipative systems. Zbl 07540356
Zhang, Yanrong; Shen, Jie
2022
Discrete maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation. Zbl 1489.65124
Shen, Jie; Zhang, Xiangxiong
2022
Generalized SAV approaches for gradient systems. Zbl 1475.65066
Cheng, Qing; Liu, Chun; Shen, Jie
2021
Bound/positivity preserving and energy stable scalar auxiliary variable schemes for dissipative systems: applications to Keller-Segel and Poisson-Nernst-Planck equations. Zbl 07364339
Huang, Fukeng; Shen, Jie
2021
Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations. Zbl 1491.65086
Shen, Jie; Xu, Jie
2021
Stability and error analysis of a class of high-order IMEX schemes for Navier-Stokes equations with periodic boundary conditions. Zbl 07453432
Huang, Fukeng; Shen, Jie
2021
Scalar auxiliary variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 07505911
Antoine, Xavier; Shen, Jie; Tang, Qinglin
2021
Efficient and accurate SAV schemes for the generalized Zakharov systems. Zbl 1465.35362
Shen, Jie; Zheng, Nan
2021
Computing interface with quasiperiodicity. Zbl 07508468
Cao, Duo; Shen, Jie; Xu, Jie
2021
A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations. Zbl 07508502
Li, Maojun; Cheng, Yongping; Shen, Jie; Zhang, Xiangxiong
2021
Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis. Zbl 1491.65111
Deng, Beichuan; Shen, Jie; Zhuang, Qingqu
2021
A new Lagrange multiplier approach for gradient flows. Zbl 1442.65211
Cheng, Qing; Liu, Chun; Shen, Jie
2020
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. Zbl 1453.65437
Cai, Jiaxiang; Shen, Jie
2020
A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. Zbl 1451.65210
Huang, Fukeng; Shen, Jie; Yang, Zhiguo
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
2020
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. Zbl 1442.65294
Li, Xiaoli; Shen, Jie
2020
Error analysis of the SAV-MAC scheme for the Navier-Stokes equations. Zbl 1452.65167
Li, Xiaoli; Shen, Jie
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
2020
Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. Zbl 1440.65192
Chen, Hongtao; Mao, Jingjing; Shen, Jie
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
2020
A spectrally accurate approximation to subdiffusion equations using the log orthogonal functions. Zbl 1434.65291
Chen, Sheng; Shen, Jie; Zhang, Zhimin; Zhou, Zhi
2020
Global constraints preserving scalar auxiliary variable schemes for gradient flows. Zbl 1456.65087
Cheng, Qing; Shen, Jie
2020
Unconditionally bound preserving and energy dissipative schemes for a class of Keller-Segel equations. Zbl 1440.65101
Shen, Jie; Xu, Jie
2020
Bound preserving and energy dissipative schemes for porous medium equation. Zbl 1436.65101
Gu, Yiqi; Shen, Jie
2020
Error estimate of Gauge-Uzawa methods for incompressible flows with variable density. Zbl 1427.76124
Chen, Hongtao; Mao, Jingjing; Shen, Jie
2020
Accurate and efficient spectral methods for elliptic PDEs in complex domains. Zbl 1440.65160
Gu, Yiqi; Shen, Jie
2020
An efficient and accurate numerical method for the spectral fractional Laplacian equation. Zbl 1433.65235
Chen, Sheng; Shen, Jie
2020
A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions. Zbl 1446.65128
Hu, Jingwei; Shen, Jie; Wang, Yingwei
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
2020
A new class of efficient and robust energy stable schemes for gradient flows. Zbl 1422.65080
Shen, Jie; Xu, Jie; Yang, Jiang
2019
Energy stability and convergence of SAV block-centered finite difference method for gradient flows. Zbl 1422.65165
Li, Xiaoli; Shen, Jie; Rui, Hongxing
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
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
2019
An efficient space-time method for time fractional diffusion equation. Zbl 1466.65214
Shen, Jie; Sheng, Chang-Tao
2019
Stability and convergence analysis of rotational velocity correction methods for the Navier-Stokes equations. Zbl 1435.65119
Chen, Feng; Shen, Jie
2019
Efficient and accurate structure preserving schemes for complex nonlinear systems. Zbl 1446.65213
Shen, Jie
2019
Distributional compatibility for change of measures. Zbl 1420.60027
Shen, Jie; Shen, Yi; Wang, Bin; Wang, Ruodu
2019
Fast structured Jacobi-Jacobi transforms. Zbl 07040627
Shen, Jie; Wang, Yingwei; Xia, Jianlin
2019
Fundamental gaps of the fractional Schrödinger operator. Zbl 1429.35195
Bao, Weizhu; Ruan, Xinran; Shen, Jie; Sheng, Changtao
2019
The scalar auxiliary variable (SAV) approach for gradient flows. Zbl 1380.65181
Shen, Jie; Xu, Jie; Yang, Jiang
2018
Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows. Zbl 1403.65047
Shen, Jie; Xu, Jie
2018
Multiple scalar auxiliary variable (MSAV) approach and its application to the phase-field vesicle membrane model. Zbl 1403.65045
Cheng, Qing; Shen, Jie
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
2018
Spectral element method with geometric mesh for two-sided fractional differential equations. Zbl 1397.65305
Mao, Zhiping; Shen, Jie
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
2018
Laguerre functions and their applications to tempered fractional differential equations on infinite intervals. Zbl 1398.65314
Chen, Sheng; Shen, Jie; Wang, Li-Lian
2018
Enriched spectral methods and applications to problems with weakly singular solutions. Zbl 1406.65123
Chen, Sheng; Shen, Jie
2018
A space-time Petrov-Galerkin spectral method for time fractional diffusion equation. Zbl 1438.65308
Sheng, Changtao; Shen, Jie
2018
A tight bound of hard thresholding. Zbl 1473.62287
Shen, Jie; Li, Ping
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
2018
Highly efficient and accurate spectral approximation of the angular Mathieu equation for any parameter values $$q$$. Zbl 1424.65119
Alici, Haydar; Shen, Jie
2018
Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy. Zbl 1475.82027
Shen, Jie; Xu, Jie
2018
Approximations on $$\mathrm{SO}(3)$$ by Wigner D-matrix and applications. Zbl 1398.65321
Shen, Jie; Xu, Jie; Zhang, Pingwen
2018
Preconditioning techniques in Chebyshev collocation method for elliptic equations. Zbl 1408.35025
Fang, Zhi-Wei; Shen, Jie; Sun, Hai-Wei
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
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
2017
Hermite spectral methods for fractional PDEs in unbounded domains. Zbl 1373.65075
Mao, Zhiping; Shen, Jie
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
2017
A hybrid spectral element method for fractional two-point boundary value problems. Zbl 1413.65307
Sheng, Changtao; Shen, Jie
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
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
2017
A nodal sparse grid spectral element method for multi-dimensional elliptic partial differential equations. Zbl 1429.65287
Rong, Zhijian; Shen, Jie; Yu, Haijun
2017
Online optimization for max-norm regularization. Zbl 1454.68132
Shen, Jie; Xu, Huan; Li, Ping
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
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
2017
Generalized Jacobi functions and their applications to fractional differential equations. Zbl 1335.65066
Chen, Sheng; Shen, Jie; Wang, Li-Lian
2016
On the maximum principle preserving schemes for the generalized Allen-Cahn equation. Zbl 1361.65059
Shen, Jie; Tang, Tao; Yang, Jiang
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
2016
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. Zbl 1352.65395
Mao, Zhiping; Shen, Jie
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
2016
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. Zbl 1352.65229
Chen, Ying; Shen, Jie
2016
Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. Zbl 1416.65482
Shen, Jie; Wang, Yingwei
2016
Efficient splitting schemes for magneto-hydrodynamic equations. Zbl 1388.76224
Choi, Heejun; Shen, Jie
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
2016
Two-phase Stefan problem with smoothed enthalpy. Zbl 1349.35433
Azaïez, M.; Jelassi, F.; Brahim, M. Mint; Shen, J.
2016
Efficient spectral-Galerkin method and analysis for elliptic PDEs with non-local boundary conditions. Zbl 1375.65159
Hu, Lina; Ma, Lina; Shen, Jie
2016
Decoupled, energy stable schemes for phase-field models of two-phase incompressible flows. Zbl 1327.65178
Shen, Jie; Yang, Xiaofeng
2015
Efficient energy stable numerical schemes for a phase field moving contact line model. Zbl 1351.76184
Shen, Jie; Yang, Xiaofeng; Yu, Haijun
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
2015
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations. Zbl 1335.65078
Liu, Fei; Shen, Jie
2015
Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. Zbl 1349.65721
Shen, Jie; Sheng, Changtao; Wang, Zhongqing
2015
A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows. Zbl 1349.76198
Dong, S.; Shen, J.
2015
Dynamic transitions of quasi-geostrophic channel flow. Zbl 1329.35232
Dijkstra, Henk; Sengul, Taylan; Shen, Jie; Wang, Shouhong
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
2015
Accurate solution and approximations of the linearized BGK equation for steady Couette flow. Zbl 1410.76412
Li, Wei; Luo, Li-Shi; Shen, Jie
2015
Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem. Zbl 1443.65306
An, Jing; Shen, Jie
2015
Spectral approximation of time-harmonic Maxwell equations in three-dimensional exterior domains. Zbl 1329.65286
Ma, Lina; Shen, Jie; Wang, Li-Lian
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.
2015
A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates. Zbl 1488.65513
Mao, Zhiping; Shen, Jie
2015
Decoupled energy stable schemes for phase-field models of two-phase complex fluids. Zbl 1288.76057
Shen, Jie; Yang, Xiaofeng
2014
Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains. Zbl 1293.65161
Shen, Jie; Wang, Li-Lian; Yu, Haijun
2014
A new spectral method for numerical solution of the unbounded rough surface scattering problem. Zbl 1349.65646
He, Ying; Li, Peijun; Shen, Jie
2014
Unconditionally stable pressure-correction schemes for a linear fluid-structure interaction problem. Zbl 1324.76040
He, Ying; Shen, Jie
2014
Efficient spectral methods for transmission eigenvalues and estimation of the index of refraction. Zbl 1313.78022
An, Jing; Shen, Jie
2014
...and 130 more Documents
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### Cited by 4,211 Authors

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

 509 Journal of Computational Physics 301 Journal of Scientific Computing 180 Applied Numerical Mathematics 154 Journal of Computational and Applied Mathematics 141 Computer Methods in Applied Mechanics and Engineering 123 Computers & Mathematics with Applications 111 Computers and Fluids 100 Applied Mathematics and Computation 97 SIAM Journal on Scientific Computing 89 Journal of Fluid Mechanics 73 Communications in Computational Physics 70 SIAM Journal on Numerical Analysis 66 Mathematics of Computation 60 Numerical Algorithms 55 International Journal of Computer Mathematics 54 Advances in Computational Mathematics 45 Numerische Mathematik 45 Applied Mathematics Letters 38 Mathematical Methods in the Applied Sciences 35 Numerical Methods for Partial Differential Equations 35 Physics of Fluids 35 Discrete and Continuous Dynamical Systems. Series B 34 Computational and Applied Mathematics 32 Communications in Nonlinear Science and Numerical Simulation 30 Journal of Mathematical Analysis and Applications 29 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 27 Advances in Applied Mathematics and Mechanics 26 International Journal for Numerical Methods in Fluids 26 Applied Mathematical Modelling 23 Mathematics and Computers in Simulation 20 Advances in Difference Equations 20 Science China. Mathematics 19 Physica D 19 Mathematical Problems in Engineering 18 Computer Physics Communications 17 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 17 Communications on Applied Mathematics and Computation 16 East Asian Journal on Applied Mathematics 15 Journal of Differential Equations 14 Abstract and Applied Analysis 13 Calcolo 13 SIAM Journal on Applied Mathematics 13 Computational Methods in Applied Mathematics 13 International Journal of Numerical Analysis and Modeling 13 Discrete and Continuous Dynamical Systems. Series S 11 BIT 11 Engineering Analysis with Boundary Elements 11 European Journal of Mechanics. B. Fluids 10 Applicable Analysis 10 Numerical Functional Analysis and Optimization 10 International Journal of Computational Fluid Dynamics 10 Nonlinear Dynamics 10 Journal of Mathematical Fluid Mechanics 10 Journal of Applied Mathematics and Computing 10 Frontiers of Mathematics in China 9 Archive for Rational Mechanics and Analysis 9 Chaos, Solitons and Fractals 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 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 Applied Mathematics 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Communications on Pure and Applied Analysis 8 Chinese Annals of Mathematics. Series B 8 Fractional Calculus & Applied Analysis 8 Nonlinear Analysis. Real World Applications 8 International Journal of Applied and Computational Mathematics 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Computational Mechanics 7 SIAM Journal on Mathematical Analysis 7 Mathematical Modelling and Analysis 7 International Journal of Computational Methods 7 S$$\vec{\text{e}}$$MA Journal 7 AIMS Mathematics 6 Acta Mechanica 6 Journal of Inequalities and Applications 6 International Journal of Nonlinear Sciences and Numerical Simulation 6 Multiscale Modeling & Simulation 6 Boundary Value Problems 6 SIAM/ASA Journal on Uncertainty Quantification 6 Journal of Function Spaces 5 Journal of Engineering Mathematics 5 Journal of Statistical Physics 5 Mathematical and Computer Modelling 5 SIAM Review 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 International Journal of Engineering Science 4 Physica A 4 Bulletin of Mathematical Biology 4 Theoretical and Computational Fluid Dynamics 4 Journal of Approximation Theory 4 Acta Applicandae Mathematicae 4 Bulletin of the Iranian Mathematical Society 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 RAIRO. Modélisation Mathématique et Analyse Numérique 4 Calculus of Variations and Partial Differential Equations ...and 206 more Serials
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### Cited in 49 Fields

 2,648 Numerical analysis (65-XX) 1,587 Partial differential equations (35-XX) 1,502 Fluid mechanics (76-XX) 191 Statistical mechanics, structure of matter (82-XX) 190 Ordinary differential equations (34-XX) 187 Mechanics of deformable solids (74-XX) 135 Approximations and expansions (41-XX) 131 Integral equations (45-XX) 116 Real functions (26-XX) 98 Biology and other natural sciences (92-XX) 95 Special functions (33-XX) 91 Calculus of variations and optimal control; optimization (49-XX) 84 Optics, electromagnetic theory (78-XX) 82 Dynamical systems and ergodic theory (37-XX) 71 Probability theory and stochastic processes (60-XX) 66 Classical thermodynamics, heat transfer (80-XX) 57 Quantum theory (81-XX) 42 Geophysics (86-XX) 40 Harmonic analysis on Euclidean spaces (42-XX) 29 Computer science (68-XX) 29 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 25 Operator theory (47-XX) 23 Systems theory; control (93-XX) 21 Linear and multilinear algebra; matrix theory (15-XX) 16 Operations research, mathematical programming (90-XX) 12 Mechanics of particles and systems (70-XX) 11 Functional analysis (46-XX) 11 Astronomy and astrophysics (85-XX) 10 Potential theory (31-XX) 9 Statistics (62-XX) 9 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 Differential geometry (53-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 General topology (54-XX)