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Luo, Zhendong

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Author ID: luo.zhendong Recent zbMATH articles by "Luo, Zhendong"
Published as: Luo, Zhendong; Luo, Z.; Luo, Zhen-dong; Luo, Zhen Dong; Luo, Zhen-Dong; Luo, ZhenDong; Luo, Z. D.
Documents Indexed: 166 Publications since 1975, including 1 Book
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Serials

20 Mathematica Numerica Sinica
12 Journal of Mathematical Analysis and Applications
12 Applied Mathematics and Mechanics. (English Edition)
7 Acta Mathematica Scientia. Series A. (Chinese Edition)
7 Acta Mathematica Scientia. Series B. (English Edition)
6 Applied Numerical Mathematics
6 Journal of Inequalities and Applications
6 Boundary Value Problems
5 Advances in Difference Equations
4 International Journal for Numerical Methods in Fluids
4 Applied Mathematics and Computation
4 Journal of Inner Mongolia University
3 Numerical Methods for Partial Differential Equations
3 Applied Mathematical Modelling
3 Chinese Journal of Numerical Mathematics and Applications
2 Modern Physics Letters A
2 Computers & Mathematics with Applications
2 Computer Methods in Applied Mechanics and Engineering
2 IEEE Transactions on Automatic Control
2 Journal of Computational and Applied Mathematics
2 Mathematics and Computers in Simulation
2 SIAM Journal on Numerical Analysis
2 Acta Mathematicae Applicatae Sinica
2 Acta Mathematicae Applicatae Sinica. English Series
2 Science in China. Series A
2 Applied Mathematics
2 Applied Mathematics. Series A (Chinese Edition)
2 AMM. Applied Mathematics and Mechanics. (English Edition)
1 Modern Physics Letters B
1 Computers and Fluids
1 IEEE Transactions on Information Theory
1 Journal of Mathematical Physics
1 Mathematical Methods in the Applied Sciences
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 International Journal for Numerical Methods in Engineering
1 Numerical Mathematics
1 Advances in Mathematics
1 Journal of Computational Mathematics
1 Journal of China University of Science and Technology
1 Applied Mathematics Letters
1 Mathematica Applicata
1 Journal of Scientific Computing
1 Journal of Integral Equations and Applications
1 Japan Journal of Industrial and Applied Mathematics
1 IEEE Transactions on Signal Processing
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Applied Mathematics. Series B (English Edition)
1 IEE Proceedings. Control Theory and Applications
1 Computational and Applied Mathematics
1 Journal on Numerical Methods and Computer Applications
1 Science in China. Series E
1 Acta Mathematica Scientia. Series A. (Chinese Edition)
1 Chinese Quarterly Journal of Mathematics
1 Communications in Nonlinear Science and Numerical Simulation
1
1 CMES. Computer Modeling in Engineering & Sciences
1 Mathematical Modelling and Analysis
1 Discrete and Continuous Dynamical Systems. Series B
1 Science in China. Series F
1 Mathematics in Science and Engineering
1 Frontiers of Mathematics in China
1 Advanced Modeling and Optimization
1 Journal of Nonlinear Science and Applications
1 Advances in Applied Mathematics and Mechanics
1 International Journal for Numerical Methods in Biomedical Engineering

Publications by Year

Citations contained in zbMATH Open

114 Publications have been cited 823 times in 270 Documents Cited by Year
A reduced-order approach to four-dimensional variational data assimilation using proper orthogonal decomposition. Zbl 1370.86002
Cao, Yanhua; Zhu, Jiang; Navon, I. M.; Luo, Zhendong
46
2007
Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model. Zbl 1173.76348
Luo, Zhendong; Zhu, Jiang; Wang, Ruiwen; Navon, I. M.
35
2007
Reduced-order modeling of the upper tropical Pacific ocean model using proper orthogonal decomposition. Zbl 1161.86002
Cao, Yanhua; Zhu, Jiang; Luo, Zhendong; Navon, I. M.
35
2006
An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems. Zbl 1161.76032
Luo, Zhendong; Chen, Jing; Navon, I. M.; Zhu, Jiang
34
2009
Mixed finite element formulation and error estimates based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations. Zbl 1391.76351
Luo, Zhendong; Chen, Jing; Navon, I. M.; Yang, Xiaozhong
33
2009
An optimizing reduced order FDS for the tropical Pacific Ocean reduced gravity model. Zbl 1205.86007
Luo, Zhendong; Chen, Jing; Zhu, Jiang; Wang, Ruiwen; Navon, I. M.
33
2007
Some reduced finite difference schemes based on a proper orthogonal decomposition technique for parabolic equations. Zbl 1193.65159
Sun, Ping; Luo, Zhendong; Zhou, Yanjie
32
2010
A reduced finite volume element formulation and numerical simulations based on POD for parabolic problems. Zbl 1227.65076
Luo, Zhendong; Xie, Zhenghui; Shang, Yueqiang; Chen, Jing
30
2011
Finite difference scheme based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations. Zbl 1134.35387
Luo, Zhendong; Wang, Ruiwen; Zhu, Jiang
27
2007
A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation. Zbl 1179.65111
Luo, Zhendong; Yang, Xiaozhong; Zhou, Yanjie
26
2009
A reduced finite element formulation based on POD method for two-dimensional solute transport problems. Zbl 1243.65123
Luo, Zhendong; Li, Hong; Zhou, Yanjie; Xie, Zhenghui
23
2012
A reduced stabilized mixed finite element formulation based on proper orthogonal decomposition for the non-stationary Navier-Stokes equations. Zbl 1242.76129
Luo, Zhendong; Du, Juan; Xie, Zhenghui; Guo, Yan
21
2011
A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation. Zbl 1169.65096
Luo, Zhendong; Zhou, Yanjie; Yang, Xiaozhong
19
2009
Mixed finite element analysis and numerical solitary solution for the RLW equation. Zbl 0927.65123
Luo, Zhendong; Liu, Ruxun
15
1998
Finite element formulation based on proper orthogonal decomposition for parabolic equations. Zbl 1183.65122
Luo, ZhenDong; Chen, Jing; Sun, Ping; Yang, XiaoZhong
15
2009
A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem. Zbl 1368.74071
Luo, Zhendong; Li, Hong; Zhou, Yanjie; Huang, Xiaoming
15
2012
A reduced-order finite difference extrapolation algorithm based on POD technique for the non-stationary Navier-Stokes equations. Zbl 1426.76478
Luo, Zhendong; Li, Hong; Sun, Ping; Gao, Junqiang
14
2013
Numerical simulation based on POD for two-dimensional solute transport problems. Zbl 1217.74082
Li, Huanrong; Luo, Zhendong; Chen, Jing
14
2011
An optimizing finite difference scheme based on proper orthogonal decomposition for CVD equations. Zbl 1429.35184
Du, Juan; Zhu, Jiang; Luo, Zhendong; Navon, I. M.
13
2011
Reduced finite difference scheme and error estimates based on POD method for non-stationary Stokes equation. Zbl 1237.65126
Luo, Zhen-dong; Ou, Qiu-lan; Xie, Zheng-hui
12
2011
A comparison of three kinds of local and parallel finite element algorithms based on two-grid discretizations for the stationary Navier-Stokes equations. Zbl 1245.76056
Shang, Yueqiang; He, Yinnian; Luo, Zhendong
11
2011
A fully discrete stabilized mixed finite volume element formulation for the non-stationary conduction-convection problem. Zbl 1304.65198
Luo, Zhendong; Li, Hong; Sun, Ping
10
2013
A POD reduced-order finite difference time-domain extrapolating scheme for the 2D Maxwell equations in a lossy medium. Zbl 1382.65252
Luo, Zhendong; Gao, Junqiang
10
2016
Reduced-order finite difference extrapolation model based on proper orthogonal decomposition for two-dimensional shallow water equations including sediment concentration. Zbl 1318.35083
Luo, Zhendong; Gao, Junqiang; Xie, Zhenghui
9
2015
A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations. Zbl 1343.76031
Luo, Zhendong
9
2014
An optimized Crank-Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation. Zbl 1458.65118
Zhou, Yanjie; Luo, Zhendong
9
2019
A stabilized fully discrete finite volume element formulation for the non-stationary Stokes equation. Zbl 1240.76002
An, Jing; Sun, Ping; Luo, Zhendong; Huang, Xiaoming
9
2011
A reduced MFE formulation based on POD for the non-stationary conduction-convection problems. Zbl 1249.65199
Luo, Zhendong; Xie, Zhenghui; Chen, Jing
9
2011
Reduced-order extrapolation spectral-finite difference scheme based on POD method and error estimation for three-dimensional parabolic equation. Zbl 1327.65210
An, Jing; Luo, Zhendong; Li, Hong; Sun, Ping
8
2015
A reduced-order extrapolated Crank-Nicolson finite spectral element method based on POD for the 2D non-stationary Boussinesq equations. Zbl 1407.65218
Luo, Zhendong; Teng, Fei; Xia, Hong
8
2019
A new space-time continuous Galerkin method with mesh modification for Sobolev equations. Zbl 1382.65335
Zhao, Zhihui; Li, Hong; Luo, Zhendong
7
2016
A fully discrete finite volume element formulation for the Sobolev equation and numerical simulations. Zbl 1265.65221
Li, Hong; Luo, Zhendong; An, Jing; Sun, Ping
7
2012
A reduced-order Crank-Nicolson finite volume element formulation based on POD method for parabolic equations. Zbl 1273.65117
Luo, Zhendong; Li, Hong; Sun, Ping
7
2013
An optimized SPDMFE extrapolation approach based on the POD technique for 2D viscoelastic wave equation. Zbl 1353.74078
Luo, Zhendong; Teng, Fei
6
2017
A parallel two-level finite element method for the Navier-Stokes equations. Zbl 1410.76196
Shang, Yue-qiang; Luo, Zhen-dong
6
2010
A finite volume element formulation and error analysis for the non-stationary conduction-convection problem. Zbl 1248.35163
Li, Hong; Luo, Zhendong; Sun, Ping; An, Jing
6
2012
A reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations. Zbl 1410.65318
Luo, Zhendong; Jin, Shiju; Chen, Jing
6
2016
A reduced-order extrapolated Crank-Nicolson finite spectral element method for the 2D non-stationary Navier-Stokes equations about vorticity-stream functions. Zbl 1432.65141
Luo, Zhendong; Jiang, Wenrui
6
2020
A reduced-order extrapolated finite difference iterative method for the Riemann-Liouville tempered fractional derivative equation. Zbl 1446.65073
Luo, Zhendong; Ren, Hulin
6
2020
A reduced-order extrapolation technique for solution coefficient vectors in the mixed finite element method for the 2D nonlinear Rosenau equation. Zbl 1434.65192
Teng, Fei; Luo, Zhendong
6
2020
Proper orthogonal decomposition-based reduced-order stabilized mixed finite volume element extrapolating model for the nonstationary incompressible Boussinesq equations. Zbl 1311.76083
Luo, Zhendong
6
2015
A reduced finite difference scheme based on proper orthogonal decomposition for the nonstationary conduction-convection problems. Zbl 1212.65327
Sun, Ping; Luo, Zhendong; Zhou, Yanjie
5
2009
A stabilized Crank-Nicolson mixed finite volume element formulation for the non-stationary incompressible Boussinesq equations. Zbl 1332.65127
Luo, Zhen Dong
5
2016
Mixed finite element analysis and numerical simulation for Burgers equation. Zbl 0933.65117
Luo, Zhendong; Liu, Ruxun
5
1999
Difference scheme and numerical simulation based on mixed finite element method for natural convection problem. Zbl 1079.76601
Luo, Zhendong; Zhu, Jiang; Xie, Zhenghui; Zhang, Guifang
5
2003
Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation. Zbl 1380.65190
Xia, Hong; Luo, Zhendong
5
2017
A stabilized mixed finite element formulation for the non-stationary incompressible Boussinesq equations. Zbl 1363.76042
Luo, Zhendong
5
2016
A highly efficient reduced-order extrapolated finite difference algorithm for time-space tempered fractional diffusion-wave equation. Zbl 1440.65093
Luo, Zhendong; Wang, Hui
5
2020
A reduced-order extrapolation algorithm based on CNLSMFE formulation and POD technique for two-dimensional Sobolev equations. Zbl 1313.65307
Liu, Qun; Teng, Fei; Luo, Zhendong
4
2014
A POD reduced-order SPDMFE extrapolating algorithm for hyperbolic equations. Zbl 1313.65267
Luo, Zhendong; Li, Hong
4
2014
A reduced-order extrapolation algorithm based on SFVE method and POD technique for non-stationary Stokes equations. Zbl 1338.76077
Luo, Zhendong
4
2014
Transformations between canonical forms for multivariable linear constant systems. Zbl 0356.93010
Luo, Z.
4
1977
A POD-based reduced-order FD extrapolating algorithm for traffic flow. Zbl 1343.76032
Luo, Zhendong; Xie, Di; Teng, Fei
4
2014
An optimizing implicit difference scheme based on proper orthogonal decomposition for the two-dimensional unsaturated soil water flow equation. Zbl 1426.76466
Di, Zhenhua; Luo, Zhendong; Xie, Zhenghui; Wang, Aiwen; Navon, I. M.
4
2012
A reduced-order extrapolated technique about the unknown coefficient vectors of solutions in the finite element method for hyperbolic type equation. Zbl 1450.65126
Luo, Zhendong; Jiang, Wenrui
4
2020
A reduced-order extrapolating Crank-Nicolson finite difference scheme for the Riesz space fractional order equations with a nonlinear source function and delay. Zbl 1449.65173
Cao, Yanhua; Luo, Zhendong
4
2018
A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation. Zbl 1427.65174
Luo, Zhendong; Teng, Fei
4
2018
A reduced-order SMFVE extrapolation algorithm based on POD technique and CN method for the non-stationary Navier-Stokes equations. Zbl 1307.65115
Luo, Zhendong
3
2015
A POD-based reduced-order TSCFE extrapolation iterative format for two-dimensional heat equations. Zbl 1411.74060
Luo, Zhendong
3
2015
A proper orthogonal decomposition based reduced-order finite difference extrapolation iterative format for 2D hyperbolic equations. Zbl 1324.65115
Teng, Fei; Luo, Zhendong; Li, Xiaobo
3
2014
Two-to-one resonant Hopf bifurcations in a quadratically nonlinear oscillator involving time delay. Zbl 1270.34186
Ji, J. C.; Li, X. Y.; Luo, Z.; Zhang, N.
3
2012
Mixed finite element methods for the shallow water equations including current and silt sedimentation. II: The discrete-time case along characteristics. Zbl 1145.76404
Luo, Zhendong; Zhu, Jiang; Zeng, Qingcun; Xie, Zhenghui
3
2004
Mixed finite element methods for the shallow water equations including current and silt sedimentation. I: The continuous-time case. Zbl 1141.76424
Luo, Zhendong; Zhu, Jiang; Zeng, Qingcun; Xie, Zhenghui
3
2004
Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations. Zbl 1422.65211
Luo, Zhendong; Teng, Fei
3
2017
Discrete Kalman filtering using a generalized companion form. Zbl 0299.93040
Luo, Z.; Bullock, T. E.
3
1975
The third order estimate of mixed finite element for the Navier-Stokes problem. Zbl 0967.76558
Luo, Zhendong
3
1995
Higher principal bundles. Zbl 1109.18007
Jardine, J. F.; Luo, Z.
3
2006
A space-time continuous Galerkin method with mesh modification for viscoelastic wave equations. Zbl 1373.65074
Zhao, Zhihui; Li, Hong; Luo, Zhendong
3
2017
Analysis of a space-time continuous Galerkin method for convection-dominated Sobolev equations. Zbl 1372.65277
Zhao, Zhihui; Li, Hong; Luo, Zhendong
3
2017
Bubble stabilization and a posteriori error estimate of MFE method for plane elasticity problems. Zbl 1115.74051
Luo, Zhendong
3
2006
A reduced-order extrapolated Crank-Nicolson collocation spectral method based on proper orthogonal decomposition for the two-dimensional viscoelastic wave equations. Zbl 1457.65146
Luo, Zhendong; Jin, Shiju
3
2020
A new reduced-order FVE algorithm based on POD method for viscoelastic equations. Zbl 1313.74040
Li, Hong; Luo, Zhendong; Gao, Junqiang
2
2013
A reduced-order MFE formulation based on POD method for parabolic equations. Zbl 1299.65232
Luo, Zhendong; Li, Lei; Sun, Ping
2
2013
A reduced-order FVE extrapolation algorithm based on proper orthogonal decomposition technique and its error analysis for Sobolev equation. Zbl 1328.65211
Luo, Zhendong; Li, Hong; Chen, Jing; Teng, Fei
2
2015
A space-time continuous finite element method for 2D viscoelastic wave equation. Zbl 1332.74047
Li, Hong; Zhao, Zhihui; Luo, Zhendong
2
2016
Nonlinear Galerkin mixed element methods for the non stationary conduction-convection problems. II: The backward one-step Euler fully discrete format. Zbl 0959.76044
Luo, Zhendong; Wang, Lieheng
2
1998
A nonlinear Galerkin mixed element method and a posteriori error estimator for the stationary Navier-Stokes equations. Zbl 1143.76481
Luo, Zhendong; Zhu, Jiang
2
2002
A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations. Zbl 1344.65088
Luo, Zhendong
2
2016
A highly efficient spectral-Galerkin method based on tensor product for fourth-order Steklov equation with boundary eigenvalue. Zbl 1347.65180
An, Jing; Bi, Hai; Luo, Zhendong
2
2016
A stabilized MFE reduced-order extrapolation model based on POD for the 2D unsteady conduction-convection problem. Zbl 1364.65230
Xia, Hong; Luo, Zhendong
2
2017
An optimized finite element extrapolating method for 2D viscoelastic wave equation. Zbl 1372.65313
Xia, Hong; Luo, Zhendong
2
2017
An optimized FD extrapolated scheme based on POD for the 2D integro-differential equation of parabolic type. Zbl 1454.65132
Luo, Zhendong
2
2020
Self-discrete finite volume element simulation for a two-dimension unsaturated soil water flow problem. Zbl 1240.76012
Li, Huanrong; Luo, Zhendong
2
2011
A Crank-Nicolson collocation spectral method for the two-dimensional viscoelastic wave equation. Zbl 1418.76037
Jin, Shiju; Luo, Zhendong
2
2019
Generalized difference methods and numerical simulation for two-dimensional viscoelastic problems. Zbl 1142.74387
Li, Huanrong; Luo, Zhendong; Li, Qian
2
2007
An extrapolation reduced-order FDS based on POD technique for a traffic flow model. Zbl 1299.65256
Luo, Zhendong; Gao, Junqiang; Sun, Ping; An, Jing
1
2013
A mixed covolume method for pseudo-hyperbolic equations. Zbl 1299.65205
Fang, Zhichao; Li, Hong; Luo, Zhendong
1
2013
A new finite volume element formulation for the non-stationary Navier-Stokes equations. Zbl 1310.65102
Luo, Zhendong
1
2014
A POD-based reduced-order CN finite element extrapolating model for unsaturated soil water flow equation. Zbl 1313.76064
Teng, Fei; Luo, Zhendong
1
2014
A high accuracy numerical method based on spectral theory of compact operator for biharmonic eigenvalue equations. Zbl 1331.65164
Luo, Zhendong
1
2016
A high accuracy spectral method based on \(\min\)/\(\max\) principle for biharmonic eigenvalue problems on a spherical domain. Zbl 1336.65185
An, Jing; Luo, Zhendong
1
2016
A fully discrete SCNFVE formulation for the non-stationary Navier-Stokes equations. Zbl 1356.76190
Luo, Zhendong; Teng, Fei
1
2014
Stabilized mixed finite element model for the 2D nonlinear incompressible viscoelastic fluid system. Zbl 1360.76148
Luo, Zhendong; Gao, Junqiang
1
2017
Implication of entropy flow for the development of a system as suggested by the life cycle of a hurricane. Zbl 1195.86009
Liu, C.; Luo, Z.; Liu, Y.; Yu, H.; Zhou, X.; Wang, D.; Ma, L.; Xu, H.
1
2010
The second order mixed finite element method of quadrilateral elements for Stokes problem in two dimensional space. Zbl 0760.76049
Luo, Zhendong
1
1990
Nonlinear Galerkin mixed element methods for the non-stationary conduction-convection problems. I: The continuous-time case. Zbl 0928.76059
Luo, Zhendong; Wang, Lieheng
1
1998
The mixed finite element method for the non stationary conduction-convection problems. Zbl 0919.76050
Luo, Zhendong
1
1998
Mixed finite element estimates for second order elliptic problems. Zbl 0797.65084
Luo, Zhendong
1
1993
A nonlinear Galerkin/Petrov-least squares mixed element method for the stationary Navier-Stokes equations. Zbl 1036.76032
Luo, Zhendong; Zhu, Jiang; Wang, Huijun
1
2002
Proper orthogonal decomposition methods for partial differential equations. Zbl 1458.65002
Luo, Zhendong; Chen, Goong
1
2019
A reduced-order extrapolated Crank-Nicolson finite spectral element method for the 2D non-stationary Navier-Stokes equations about vorticity-stream functions. Zbl 1432.65141
Luo, Zhendong; Jiang, Wenrui
6
2020
A reduced-order extrapolated finite difference iterative method for the Riemann-Liouville tempered fractional derivative equation. Zbl 1446.65073
Luo, Zhendong; Ren, Hulin
6
2020
A reduced-order extrapolation technique for solution coefficient vectors in the mixed finite element method for the 2D nonlinear Rosenau equation. Zbl 1434.65192
Teng, Fei; Luo, Zhendong
6
2020
A highly efficient reduced-order extrapolated finite difference algorithm for time-space tempered fractional diffusion-wave equation. Zbl 1440.65093
Luo, Zhendong; Wang, Hui
5
2020
A reduced-order extrapolated technique about the unknown coefficient vectors of solutions in the finite element method for hyperbolic type equation. Zbl 1450.65126
Luo, Zhendong; Jiang, Wenrui
4
2020
A reduced-order extrapolated Crank-Nicolson collocation spectral method based on proper orthogonal decomposition for the two-dimensional viscoelastic wave equations. Zbl 1457.65146
Luo, Zhendong; Jin, Shiju
3
2020
An optimized FD extrapolated scheme based on POD for the 2D integro-differential equation of parabolic type. Zbl 1454.65132
Luo, Zhendong
2
2020
The Crank-Nicolson finite spectral element method and numerical simulations for 2D non-stationary Navier-Stokes equations. Zbl 1452.65278
Luo, Zhendong; Jiang, Wenrui
1
2020
An optimized Crank-Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation. Zbl 1458.65118
Zhou, Yanjie; Luo, Zhendong
9
2019
A reduced-order extrapolated Crank-Nicolson finite spectral element method based on POD for the 2D non-stationary Boussinesq equations. Zbl 1407.65218
Luo, Zhendong; Teng, Fei; Xia, Hong
8
2019
A Crank-Nicolson collocation spectral method for the two-dimensional viscoelastic wave equation. Zbl 1418.76037
Jin, Shiju; Luo, Zhendong
2
2019
Proper orthogonal decomposition methods for partial differential equations. Zbl 1458.65002
Luo, Zhendong; Chen, Goong
1
2019
A 3D OpenFOAM based finite volume solver for incompressible Oldroyd-B model with infinity relaxation time. Zbl 1456.76081
Tian, Jing; Cai, Mingchao; Luo, Zhendong; You, Yuncheng; Chen, Goong
1
2019
A reduced-order extrapolating Crank-Nicolson finite difference scheme for the Riesz space fractional order equations with a nonlinear source function and delay. Zbl 1449.65173
Cao, Yanhua; Luo, Zhendong
4
2018
A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation. Zbl 1427.65174
Luo, Zhendong; Teng, Fei
4
2018
A POD-based reduced-order Crank-Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations. Zbl 07316185
Luo, Zhendong; Teng, Fei; Chen, Jing
1
2018
An optimized SPDMFE extrapolation approach based on the POD technique for 2D viscoelastic wave equation. Zbl 1353.74078
Luo, Zhendong; Teng, Fei
6
2017
Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation. Zbl 1380.65190
Xia, Hong; Luo, Zhendong
5
2017
Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations. Zbl 1422.65211
Luo, Zhendong; Teng, Fei
3
2017
A space-time continuous Galerkin method with mesh modification for viscoelastic wave equations. Zbl 1373.65074
Zhao, Zhihui; Li, Hong; Luo, Zhendong
3
2017
Analysis of a space-time continuous Galerkin method for convection-dominated Sobolev equations. Zbl 1372.65277
Zhao, Zhihui; Li, Hong; Luo, Zhendong
3
2017
A stabilized MFE reduced-order extrapolation model based on POD for the 2D unsteady conduction-convection problem. Zbl 1364.65230
Xia, Hong; Luo, Zhendong
2
2017
An optimized finite element extrapolating method for 2D viscoelastic wave equation. Zbl 1372.65313
Xia, Hong; Luo, Zhendong
2
2017
Stabilized mixed finite element model for the 2D nonlinear incompressible viscoelastic fluid system. Zbl 1360.76148
Luo, Zhendong; Gao, Junqiang
1
2017
A natural boundary element method for the Sobolev equation in the 2D unbounded domain. Zbl 1422.65431
Teng, Fei; Luo, Zhendong; Yang, Jing
1
2017
An optimized finite difference Crank-Nicolson iterative scheme for the 2D Sobolev equation. Zbl 1422.65191
Xia, Hong; Luo, Zhendong
1
2017
A stabilized Crank-Nicolson mixed finite element method for non-stationary parabolized Navier-Stokes equations. Zbl 1368.65214
Zhou, Yan-jie; Teng, Fei; Luo, Zhen-dong
1
2017
A POD reduced-order finite difference time-domain extrapolating scheme for the 2D Maxwell equations in a lossy medium. Zbl 1382.65252
Luo, Zhendong; Gao, Junqiang
10
2016
A new space-time continuous Galerkin method with mesh modification for Sobolev equations. Zbl 1382.65335
Zhao, Zhihui; Li, Hong; Luo, Zhendong
7
2016
A reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations. Zbl 1410.65318
Luo, Zhendong; Jin, Shiju; Chen, Jing
6
2016
A stabilized Crank-Nicolson mixed finite volume element formulation for the non-stationary incompressible Boussinesq equations. Zbl 1332.65127
Luo, Zhen Dong
5
2016
A stabilized mixed finite element formulation for the non-stationary incompressible Boussinesq equations. Zbl 1363.76042
Luo, Zhendong
5
2016
A space-time continuous finite element method for 2D viscoelastic wave equation. Zbl 1332.74047
Li, Hong; Zhao, Zhihui; Luo, Zhendong
2
2016
A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations. Zbl 1344.65088
Luo, Zhendong
2
2016
A highly efficient spectral-Galerkin method based on tensor product for fourth-order Steklov equation with boundary eigenvalue. Zbl 1347.65180
An, Jing; Bi, Hai; Luo, Zhendong
2
2016
A high accuracy numerical method based on spectral theory of compact operator for biharmonic eigenvalue equations. Zbl 1331.65164
Luo, Zhendong
1
2016
A high accuracy spectral method based on \(\min\)/\(\max\) principle for biharmonic eigenvalue problems on a spherical domain. Zbl 1336.65185
An, Jing; Luo, Zhendong
1
2016
Reduced-order finite difference extrapolation model based on proper orthogonal decomposition for two-dimensional shallow water equations including sediment concentration. Zbl 1318.35083
Luo, Zhendong; Gao, Junqiang; Xie, Zhenghui
9
2015
Reduced-order extrapolation spectral-finite difference scheme based on POD method and error estimation for three-dimensional parabolic equation. Zbl 1327.65210
An, Jing; Luo, Zhendong; Li, Hong; Sun, Ping
8
2015
Proper orthogonal decomposition-based reduced-order stabilized mixed finite volume element extrapolating model for the nonstationary incompressible Boussinesq equations. Zbl 1311.76083
Luo, Zhendong
6
2015
A reduced-order SMFVE extrapolation algorithm based on POD technique and CN method for the non-stationary Navier-Stokes equations. Zbl 1307.65115
Luo, Zhendong
3
2015
A POD-based reduced-order TSCFE extrapolation iterative format for two-dimensional heat equations. Zbl 1411.74060
Luo, Zhendong
3
2015
A reduced-order FVE extrapolation algorithm based on proper orthogonal decomposition technique and its error analysis for Sobolev equation. Zbl 1328.65211
Luo, Zhendong; Li, Hong; Chen, Jing; Teng, Fei
2
2015
A stabilized Crank-Nicolson mixed finite volume element formulation for the non-stationary parabolized Navier-Stokes equations. Zbl 1363.76041
Luo, Zhendong
1
2015
The numerical simulations based on the NND finite difference scheme for shallow water wave equations including sediment concentration. Zbl 1423.76316
Luo, Zhendong; Gao, Junqiang
1
2015
A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations. Zbl 1343.76031
Luo, Zhendong
9
2014
A reduced-order extrapolation algorithm based on CNLSMFE formulation and POD technique for two-dimensional Sobolev equations. Zbl 1313.65307
Liu, Qun; Teng, Fei; Luo, Zhendong
4
2014
A POD reduced-order SPDMFE extrapolating algorithm for hyperbolic equations. Zbl 1313.65267
Luo, Zhendong; Li, Hong
4
2014
A reduced-order extrapolation algorithm based on SFVE method and POD technique for non-stationary Stokes equations. Zbl 1338.76077
Luo, Zhendong
4
2014
A POD-based reduced-order FD extrapolating algorithm for traffic flow. Zbl 1343.76032
Luo, Zhendong; Xie, Di; Teng, Fei
4
2014
A proper orthogonal decomposition based reduced-order finite difference extrapolation iterative format for 2D hyperbolic equations. Zbl 1324.65115
Teng, Fei; Luo, Zhendong; Li, Xiaobo
3
2014
A new finite volume element formulation for the non-stationary Navier-Stokes equations. Zbl 1310.65102
Luo, Zhendong
1
2014
A POD-based reduced-order CN finite element extrapolating model for unsaturated soil water flow equation. Zbl 1313.76064
Teng, Fei; Luo, Zhendong
1
2014
A fully discrete SCNFVE formulation for the non-stationary Navier-Stokes equations. Zbl 1356.76190
Luo, Zhendong; Teng, Fei
1
2014
A reduced-order finite difference extrapolation algorithm based on POD technique for the non-stationary Navier-Stokes equations. Zbl 1426.76478
Luo, Zhendong; Li, Hong; Sun, Ping; Gao, Junqiang
14
2013
A fully discrete stabilized mixed finite volume element formulation for the non-stationary conduction-convection problem. Zbl 1304.65198
Luo, Zhendong; Li, Hong; Sun, Ping
10
2013
A reduced-order Crank-Nicolson finite volume element formulation based on POD method for parabolic equations. Zbl 1273.65117
Luo, Zhendong; Li, Hong; Sun, Ping
7
2013
A new reduced-order FVE algorithm based on POD method for viscoelastic equations. Zbl 1313.74040
Li, Hong; Luo, Zhendong; Gao, Junqiang
2
2013
A reduced-order MFE formulation based on POD method for parabolic equations. Zbl 1299.65232
Luo, Zhendong; Li, Lei; Sun, Ping
2
2013
An extrapolation reduced-order FDS based on POD technique for a traffic flow model. Zbl 1299.65256
Luo, Zhendong; Gao, Junqiang; Sun, Ping; An, Jing
1
2013
A mixed covolume method for pseudo-hyperbolic equations. Zbl 1299.65205
Fang, Zhichao; Li, Hong; Luo, Zhendong
1
2013
A reduced finite element formulation based on POD method for two-dimensional solute transport problems. Zbl 1243.65123
Luo, Zhendong; Li, Hong; Zhou, Yanjie; Xie, Zhenghui
23
2012
A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem. Zbl 1368.74071
Luo, Zhendong; Li, Hong; Zhou, Yanjie; Huang, Xiaoming
15
2012
A fully discrete finite volume element formulation for the Sobolev equation and numerical simulations. Zbl 1265.65221
Li, Hong; Luo, Zhendong; An, Jing; Sun, Ping
7
2012
A finite volume element formulation and error analysis for the non-stationary conduction-convection problem. Zbl 1248.35163
Li, Hong; Luo, Zhendong; Sun, Ping; An, Jing
6
2012
An optimizing implicit difference scheme based on proper orthogonal decomposition for the two-dimensional unsaturated soil water flow equation. Zbl 1426.76466
Di, Zhenhua; Luo, Zhendong; Xie, Zhenghui; Wang, Aiwen; Navon, I. M.
4
2012
Two-to-one resonant Hopf bifurcations in a quadratically nonlinear oscillator involving time delay. Zbl 1270.34186
Ji, J. C.; Li, X. Y.; Luo, Z.; Zhang, N.
3
2012
A new mixed finite element formulation and error estimates for parabolic equations. Zbl 1289.65224
Li, Lei; Sun, Ping; Luo, Zhendong
1
2012
A reduced FE formulation based on POD method for hyperbolic equations. Zbl 1274.65273
Luo, Zhendong; Ou, Qiulan; Wu, Jiarong; Xie, Zhenghui
1
2012
A reduced finite volume element formulation and numerical simulations based on POD for parabolic problems. Zbl 1227.65076
Luo, Zhendong; Xie, Zhenghui; Shang, Yueqiang; Chen, Jing
30
2011
A reduced stabilized mixed finite element formulation based on proper orthogonal decomposition for the non-stationary Navier-Stokes equations. Zbl 1242.76129
Luo, Zhendong; Du, Juan; Xie, Zhenghui; Guo, Yan
21
2011
Numerical simulation based on POD for two-dimensional solute transport problems. Zbl 1217.74082
Li, Huanrong; Luo, Zhendong; Chen, Jing
14
2011
An optimizing finite difference scheme based on proper orthogonal decomposition for CVD equations. Zbl 1429.35184
Du, Juan; Zhu, Jiang; Luo, Zhendong; Navon, I. M.
13
2011
Reduced finite difference scheme and error estimates based on POD method for non-stationary Stokes equation. Zbl 1237.65126
Luo, Zhen-dong; Ou, Qiu-lan; Xie, Zheng-hui
12
2011
A comparison of three kinds of local and parallel finite element algorithms based on two-grid discretizations for the stationary Navier-Stokes equations. Zbl 1245.76056
Shang, Yueqiang; He, Yinnian; Luo, Zhendong
11
2011
A stabilized fully discrete finite volume element formulation for the non-stationary Stokes equation. Zbl 1240.76002
An, Jing; Sun, Ping; Luo, Zhendong; Huang, Xiaoming
9
2011
A reduced MFE formulation based on POD for the non-stationary conduction-convection problems. Zbl 1249.65199
Luo, Zhendong; Xie, Zhenghui; Chen, Jing
9
2011
Self-discrete finite volume element simulation for a two-dimension unsaturated soil water flow problem. Zbl 1240.76012
Li, Huanrong; Luo, Zhendong
2
2011
A reduced second order time accurate finite element formulation of time second order central difference based on POD approach for parabolic equations. Zbl 1249.65206
Teng, Fei; Sun, Ping; Luo, Zhendong
1
2011
Some reduced finite difference schemes based on a proper orthogonal decomposition technique for parabolic equations. Zbl 1193.65159
Sun, Ping; Luo, Zhendong; Zhou, Yanjie
32
2010
A parallel two-level finite element method for the Navier-Stokes equations. Zbl 1410.76196
Shang, Yue-qiang; Luo, Zhen-dong
6
2010
Implication of entropy flow for the development of a system as suggested by the life cycle of a hurricane. Zbl 1195.86009
Liu, C.; Luo, Z.; Liu, Y.; Yu, H.; Zhou, X.; Wang, D.; Ma, L.; Xu, H.
1
2010
An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems. Zbl 1161.76032
Luo, Zhendong; Chen, Jing; Navon, I. M.; Zhu, Jiang
34
2009
Mixed finite element formulation and error estimates based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations. Zbl 1391.76351
Luo, Zhendong; Chen, Jing; Navon, I. M.; Yang, Xiaozhong
33
2009
A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation. Zbl 1179.65111
Luo, Zhendong; Yang, Xiaozhong; Zhou, Yanjie
26
2009
A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation. Zbl 1169.65096
Luo, Zhendong; Zhou, Yanjie; Yang, Xiaozhong
19
2009
Finite element formulation based on proper orthogonal decomposition for parabolic equations. Zbl 1183.65122
Luo, ZhenDong; Chen, Jing; Sun, Ping; Yang, XiaoZhong
15
2009
A reduced finite difference scheme based on proper orthogonal decomposition for the nonstationary conduction-convection problems. Zbl 1212.65327
Sun, Ping; Luo, Zhendong; Zhou, Yanjie
5
2009
A Petrov least squares mixed finite element method for the non-stationary conduction convection problems. Zbl 1199.65342
Sun, Ping; Luo, Zhendong; Chen, Jing
1
2009
A reduced-order approach to four-dimensional variational data assimilation using proper orthogonal decomposition. Zbl 1370.86002
Cao, Yanhua; Zhu, Jiang; Navon, I. M.; Luo, Zhendong
46
2007
Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model. Zbl 1173.76348
Luo, Zhendong; Zhu, Jiang; Wang, Ruiwen; Navon, I. M.
35
2007
An optimizing reduced order FDS for the tropical Pacific Ocean reduced gravity model. Zbl 1205.86007
Luo, Zhendong; Chen, Jing; Zhu, Jiang; Wang, Ruiwen; Navon, I. M.
33
2007
Finite difference scheme based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations. Zbl 1134.35387
Luo, Zhendong; Wang, Ruiwen; Zhu, Jiang
27
2007
Generalized difference methods and numerical simulation for two-dimensional viscoelastic problems. Zbl 1142.74387
Li, Huanrong; Luo, Zhendong; Li, Qian
2
2007
Galerkin-Petrov least squares mixed element method for stationary incompressible magnetohydrodynamics. Zbl 1231.65214
Luo, Zhen-Dong; Mao, Yun-Kui; Zhu, Jiang
1
2007
Reduced-order modeling of the upper tropical Pacific ocean model using proper orthogonal decomposition. Zbl 1161.86002
Cao, Yanhua; Zhu, Jiang; Luo, Zhendong; Navon, I. M.
35
2006
Higher principal bundles. Zbl 1109.18007
Jardine, J. F.; Luo, Z.
3
2006
Bubble stabilization and a posteriori error estimate of MFE method for plane elasticity problems. Zbl 1115.74051
Luo, Zhendong
3
2006
Mixed finite element methods for the shallow water equations including current and silt sedimentation. II: The discrete-time case along characteristics. Zbl 1145.76404
Luo, Zhendong; Zhu, Jiang; Zeng, Qingcun; Xie, Zhenghui
3
2004
Mixed finite element methods for the shallow water equations including current and silt sedimentation. I: The continuous-time case. Zbl 1141.76424
Luo, Zhendong; Zhu, Jiang; Zeng, Qingcun; Xie, Zhenghui
3
2004
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Cited by 368 Authors

66 Luo, Zhendong
25 Li, Hong
17 Navon, Ionel Michael
12 Abbaszadeh, Mostafa
12 Dehghan Takht Fooladi, Mehdi
12 Iliescu, Traian
12 Teng, Fei
11 Huang, Pengzhan
11 Liu, Yang
10 Fang, Fangxin
10 Li, Huanrong
10 Si, Zhiyong
9 He, Yinnian
9 Pain, Christopher C.
9 Shang, Yueqiang
9 Zhou, Yanjie
8 Zhu, Jiang
7 Chen, Jing
7 Hou, Yanren
7 Sun, Ping
7 Wang, Zhu
7 Xie, Zhenghui
6 Feng, Xinlong
6 Xia, Hong
5 Buchan, Andrew G.
5 Gao, Junqiang
5 Shi, Dongyang
5 Zhang, Yunzhang
5 Zhao, Zhihui
4 An, Jing
4 Du, Juan
4 Fang, Zhichao
4 He, Siriguleng
4 Song, Zhengyuan
4 Wang, Jinfeng
3 Allison, P. A.
3 Borggaard, Jeff T.
3 Chen, Xiao
3 Durlofsky, Louis J.
3 Gao, Wei
3 Goddard, A. J. H.
3 Gorman, Gerard J.
3 Heemink, Arnold Willem
3 Huang, Ting-Zhu
3 Lanteri, Stéphane
3 Li, Jian
3 Li, Kun
3 Li, Liang
3 Piggott, Matthew D.
3 Ramos, Juan I.
3 Rebholz, Leo G.
3 Ruiz-Baier, Ricardo
3 Xiao, Dianshi
3 Yang, Xiaozhong
2 Akhtar, Imran
2 Allery, Cyrille
2 Altaf, M. Umer
2 Ammar, Amine
2 Biegler, Lorenz T.
2 Cao, Yanhua
2 Cardoso, M. A.
2 Chen, Huanzhen
2 Dağ, İdris
2 Di, Zhenhua
2 Du, Yanwei
2 Dumon, Antoine
2 Ghaffari, Rezvan
2 Ghoreishi, Farideh
2 Hoteit, Ibrahim
2 Hu, Xiaohui
2 Jiang, Wenrui
2 Li, Yukun
2 Liu, Jincun
2 Liu, Qian
2 Ma, Xiaoling
2 Mao, Yunkui
2 Mei, Liquan
2 Qin, Jin
2 Quarteroni, Alfio M.
2 Rubino, Samuele
2 Saka, Bülent
2 Sandu, Adrian
2 Schneier, Michael
2 Shu, Yu
2 Singler, John R.
2 Wang, Aiwen
2 Wang, Kun
2 Xie, Xuping
2 Yang, Jing
2 Zhao, Jianping
2 Zhao, Jie
2 Zhu, Shengfeng
1 Abdi, Narjes
1 Adel, Waleed
1 Agarwal, Anshul
1 Ahmadi, Goodarz
1 Akella, Srinivas
1 Akkari, Nissrine
1 Alzabut, Jehad O.
1 Aminikhah, Hossein
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Cited in 80 Serials

20 Applied Numerical Mathematics
18 Journal of Mathematical Analysis and Applications
17 Computer Methods in Applied Mechanics and Engineering
16 Journal of Computational Physics
14 Computers & Mathematics with Applications
13 Applied Mathematics and Computation
10 International Journal for Numerical Methods in Fluids
9 Journal of Computational and Applied Mathematics
9 Journal of Scientific Computing
8 Applied Mathematics and Mechanics. (English Edition)
6 Numerical Methods for Partial Differential Equations
6 Applied Mathematical Modelling
5 Computers and Fluids
5 Engineering Analysis with Boundary Elements
5 Mathematical Problems in Engineering
5 Journal of Inequalities and Applications
5 Advances in Difference Equations
5 Boundary Value Problems
5 AMM. Applied Mathematics and Mechanics. (English Edition)
4 International Journal for Numerical Methods in Engineering
4 Communications in Nonlinear Science and Numerical Simulation
3 Applied Mathematics. Series B (English Edition)
3 Advances in Computational Mathematics
2 Journal of the Franklin Institute
2 Mathematical Methods in the Applied Sciences
2 Computing
2 SIAM Journal on Numerical Analysis
2 Acta Mathematicae Applicatae Sinica. English Series
2 International Journal of Computer Mathematics
2 Numerical Linear Algebra with Applications
2 Computational and Applied Mathematics
2 Abstract and Applied Analysis
2 Computational Geosciences
2 Mathematical Modelling and Analysis
2 Journal of Applied Mathematics
2 Journal of Numerical Mathematics
2 Journal of Applied Mathematics and Computing
2 International Journal of Computational Methods
2 Frontiers of Mathematics in China
1 Acta Mechanica
1 Journal of Engineering Mathematics
1 Mathematics of Computation
1 Chaos, Solitons and Fractals
1 Mathematics and Computers in Simulation
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Numerical Functional Analysis and Optimization
1 Numerische Mathematik
1 Results in Mathematics
1 Acta Applicandae Mathematicae
1 Applied Mathematics Letters
1 Mathematical and Computer Modelling
1 SIAM Journal on Matrix Analysis and Applications
1 Journal of Integral Equations and Applications
1 Science in China. Series A
1 Japan Journal of Industrial and Applied Mathematics
1 Applications of Mathematics
1 Numerical Algorithms
1 Journal of Dynamics and Differential Equations
1 SIAM Journal on Scientific Computing
1 Communications in Numerical Methods in Engineering
1 Russian Journal of Mathematical Physics
1 International Journal of Numerical Methods for Heat & Fluid Flow
1 Science in China. Series E
1 International Journal of Computational Fluid Dynamics
1 Differential Equations and Dynamical Systems
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Discrete Dynamics in Nature and Society
1 Optimization and Engineering
1 Lobachevskii Journal of Mathematics
1 Discrete and Continuous Dynamical Systems. Series B
1 Thai Journal of Mathematics
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1 Mathematical Biosciences and Engineering
1 Journal of Nonlinear Science and Applications
1 Science China. Mathematics
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1 Journal of Applied Analysis and Computation
1 Mathematical Sciences
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