Edit Profile (opens in new tab) Luo, Zhendong Co-Author Distance Author ID: luo.zhendong Published as: Luo, Zhendong; Luo, Zhen Dong; Luo, Zhen-dong; Luo, Zhen-Dong; Luo, ZhenDong more...less Documents Indexed: 177 Publications since 1990, including 1 Book Co-Authors: 68 Co-Authors with 150 Joint Publications 2,131 Co-Co-Authors all top 5 Co-Authors 26 single-authored 29 Sun, Ping 27 Teng, Fei 22 Li, Hong 19 Zhu, Jiang 17 Chen, Jing 15 Xie, Zhenghui 15 Zhou, Yanjie 13 An, Jing 9 Navon, Ionel Michael 7 Gao, Junqiang 6 Jin, Shiju 6 Xia, Hong 5 Li, Huanrong 5 Yang, Xiaozhong 5 Zhao, Zhihui 4 Shang, Yueqiang 4 Wang, Lieheng 3 Cao, Yanhua 3 Jiang, Wenrui 3 Liu, Ruxun 3 Wang, Ruiwen 3 Yang, Jing 3 Zeng, Qingcun 3 Zeng, Yihui 2 Chen, Goong 2 Di, Zhenhua 2 Du, Juan 2 Fang, Zhichao 2 Huang, Xiaoming 2 Li, Lei 2 Li, Yuejie 2 Liu, Qun 2 Lu, Xiu Min 2 Mao, Yunkui 2 Ou, Qiulan 2 Ren, Hulin 2 Tian, Xiangjun 2 Wang, Hui 1 Bi, Hai 1 Cai, Mingchao 1 Deng, Qiuxiang 1 Fan, Yiting 1 Guo, Yan 1 He, Qingfang 1 He, Yinnian 1 Li, Qian 1 Li, Xianchong 1 Li, Xiaobo 1 Li, Yaru 1 Liang, Ye 1 Lin, Fubiao 1 Liu, Changan 1 Liu, Xiangdong 1 Liu, Yang 1 Ren, Shanjing 1 Tian, Jing 1 Wang, Aiwen 1 Wang, Huijun 1 Wang, Jingliang 1 Wu, Jiarong 1 Wu, Yijie 1 Xie, Di 1 You, Yuncheng 1 Zhang, Guifang 1 Zhang, Guiming 1 Zhang, Yanan 1 Zhu, Taiying 1 Zhu, Zhu all top 5 Serials 27 Mathematica Numerica Sinica 14 Journal of Mathematical Analysis and Applications 12 Applied Mathematics and Mechanics. (English Edition) 10 Journal of Inequalities and Applications 8 Boundary Value Problems 7 Applied Numerical Mathematics 7 Acta Mathematica Scientia. Series A. (Chinese Edition) 7 Acta Mathematica Scientia. Series B. (English Edition) 6 Advances in Difference Equations 5 Applied Mathematics and Computation 5 Numerical Methods for Partial Differential Equations 4 International Journal for Numerical Methods in Fluids 4 Journal of Inner Mongolia University 3 Chinese Journal of Numerical Mathematics and Applications 3 Scientia Sinica. Mathematica 2 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 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 Mathematical Modelling 2 Applied Mathematics 2 Applied Mathematics. Series A (Chinese Edition) 2 Mathematical Modelling and Analysis 2 Advances in Applied Mathematics and Mechanics 2 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Computers and Fluids 1 Journal of Computational Physics 1 Mathematical Methods in the Applied Sciences 1 International Journal for Numerical Methods in Engineering 1 Numerical Mathematics 1 Advances in Mathematics (Beijing) 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 Applied Mathematics. Series B (English Edition) 1 Computational and Applied Mathematics 1 Journal on Numerical Methods and Computer Applications 1 Science in China. Series E 1 International Journal of Computational Fluid Dynamics 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Chinese Quarterly Journal of Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 CMES. Computer Modeling in Engineering & Sciences 1 Discrete and Continuous Dynamical Systems. Series B 1 Mathematics in Science and Engineering 1 Frontiers of Mathematics in China 1 Journal of Nonlinear Science and Applications 1 International Journal for Numerical Methods in Biomedical Engineering all top 5 Fields 159 Numerical analysis (65-XX) 87 Partial differential equations (35-XX) 67 Fluid mechanics (76-XX) 14 Mechanics of deformable solids (74-XX) 10 Geophysics (86-XX) 5 Classical thermodynamics, heat transfer (80-XX) 2 Real functions (26-XX) 2 Approximations and expansions (41-XX) 2 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 136 Publications have been cited 1,334 times in 452 Documents Cited by ▼ Year ▼ An optimized Crank-Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation. Zbl 1458.65118 Zhou, Yanjie; Luo, Zhendong 58 2019 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 58 2007 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 49 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. 44 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 42 2010 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. 39 2007 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 38 2011 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. 37 2006 An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems. Zbl 1161.76032 Luo, Zhendong; Chen, Jing; Navon, I. M.; Zhu, Jiang 36 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 35 2012 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 32 2009 Finite difference scheme based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations. Zbl 1134.35387 Luo, Zhendong; Wang, Ruiwen; Zhu, Jiang 30 2007 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 24 2011 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 23 2013 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 22 2019 A highly efficient reduced-order extrapolated finite difference algorithm for time-space tempered fractional diffusion-wave equation. Zbl 1440.65093 Luo, Zhendong; Wang, Hui 22 2020 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 21 2012 A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation. Zbl 1169.65096 Luo, Zhendong; Zhou, Yanjie; Yang, Xiaozhong 21 2009 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 18 2015 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 18 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 18 2011 Numerical simulation based on POD for two-dimensional solute transport problems. Zbl 1217.74082 Li, Huanrong; Luo, Zhendong; Chen, Jing 18 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. 17 2011 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 16 2016 A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation. Zbl 1427.65174 Luo, Zhendong; Teng, Fei 16 2018 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 16 2020 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 new space-time continuous Galerkin method with mesh modification for Sobolev equations. Zbl 1382.65335 Zhao, Zhihui; Li, Hong; Luo, Zhendong 15 2016 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 15 2020 A reduced-order extrapolated finite difference iterative method for the Riemann-Liouville tempered fractional derivative equation. Zbl 1446.65073 Luo, Zhendong; Ren, Hulin 15 2020 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 14 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 13 2016 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 13 2013 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 13 2020 An optimized SPDMFE extrapolation approach based on the POD technique for 2D viscoelastic wave equation. Zbl 1353.74078 Luo, Zhendong; Teng, Fei 12 2017 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 11 2015 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 11 2011 A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations. Zbl 1343.76031 Luo, Zhendong 11 2014 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 11 2020 A space-time continuous finite element method for 2D viscoelastic wave equation. Zbl 1332.74047 Li, Hong; Zhao, Zhihui; Luo, Zhendong 10 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 10 2012 A POD-based reduced-order stabilized Crank-Nicolson MFE formulation for the non-stationary parabolized Navier-Stokes equations. Zbl 1488.65444 Luo, Zhendong 10 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 9 2015 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 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 9 2014 A POD-based reduced-order Crank-Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations. Zbl 1484.65193 Luo, Zhendong; Teng, Fei; Chen, Jing 9 2018 Analysis of a space-time continuous Galerkin method for convection-dominated Sobolev equations. Zbl 1372.65277 Zhao, Zhihui; Li, Hong; Luo, Zhendong 8 2017 A reduced-order extrapolation spectral-finite difference scheme based on the POD method for 2D second-order hyperbolic equations. Zbl 1488.65265 Luo, Zhendong; Jin, Shiju 8 2017 A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems. Zbl 1490.65171 Luo, Zhendong; Li, Hong; Sun, Ping; An, Jing; Navon, Ionel Michael 8 2013 A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation. Zbl 1458.35381 Zhou, Yanjie; Zhang, Yanan; Liang, Ye; Luo, Zhendong 8 2021 A stabilized Crank-Nicolson mixed finite volume element formulation for the non-stationary incompressible Boussinesq equations. Zbl 1332.65127 Luo, Zhen Dong 8 2016 Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation. Zbl 1380.65190 Xia, Hong; Luo, Zhendong 7 2017 Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations. Zbl 1422.65211 Luo, Zhendong; Teng, Fei 7 2017 A POD-based reduced-order TSCFE extrapolation iterative format for two-dimensional heat equations. Zbl 1411.74060 Luo, Zhendong 7 2015 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 7 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. 7 2012 A stabilized MFE reduced-order extrapolation model based on POD for the 2D unsteady conduction-convection problem. Zbl 1364.65230 Xia, Hong; Luo, Zhendong 7 2017 A parallel two-level finite element method for the Navier-Stokes equations. Zbl 1410.76196 Shang, Yue-qiang; Luo, Zhen-dong 7 2010 Mixed finite element analysis and numerical simulation for Burgers equation. Zbl 0933.65117 Luo, Zhendong; Liu, Ruxun 6 1999 A stabilized mixed finite element formulation for the non-stationary incompressible Boussinesq equations. Zbl 1363.76042 Luo, Zhendong 6 2016 Proper orthogonal decomposition methods for partial differential equations. Zbl 1458.65002 Luo, Zhendong; Chen, Goong 6 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 6 2018 A reduced-order extrapolation algorithm based on SFVE method and POD technique for non-stationary Stokes equations. Zbl 1338.76077 Luo, Zhendong 6 2014 A reduced second-order time accurate finite element formulation based on POD for parabolic equations. Zbl 1488.65445 Luo, Zhendong; Chen, Jing; Xie, Zhenghui; An, Jing; Sun, Ping 6 2011 A Crank-Nicolson collocation spectral method for the two-dimensional telegraph equations. Zbl 1498.65181 Zhou, Yanjie; Luo, Zhendong 6 2018 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 5 2016 A space-time continuous Galerkin method with mesh modification for viscoelastic wave equations. Zbl 1373.65074 Zhao, Zhihui; Li, Hong; Luo, Zhendong 5 2017 A Crank-Nicolson collocation spectral method for the two-dimensional viscoelastic wave equation. Zbl 1418.76037 Jin, Shiju; Luo, Zhendong 5 2019 A reduced-order extrapolated natural boundary element method based on POD for the parabolic equation in the 2D unbounded domain. Zbl 1438.65309 Teng, Fei; Luo, Zhen Dong; Yang, Jing 5 2019 An optimized finite difference Crank-Nicolson iterative scheme for the 2D Sobolev equation. Zbl 1422.65191 Xia, Hong; Luo, Zhendong 5 2017 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 5 2014 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 5 2015 A POD reduced-order SPDMFE extrapolating algorithm for hyperbolic equations. Zbl 1313.65267 Luo, Zhendong; Li, Hong 5 2014 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 A POD-based reduced-order FD extrapolating algorithm for traffic flow. Zbl 1343.76032 Luo, Zhendong; Xie, Di; Teng, Fei 5 2014 A reduced-order extrapolating collocation spectral method based on POD for the 2D Sobolev equations. Zbl 1513.65409 Jin, Shiju; Luo, Zhendong 5 2019 A POD-based reduced-order finite difference extrapolating model with fully second-order accuracy for non-stationary Stokes equations. Zbl 1507.65142 Luo, Zhendong; Teng, Fei; Di, Zhenhua 5 2014 A least-squares Galerkin/Petrov mixed finite element method for stationary conduction-convection problems. Zbl 1495.65218 Luo, Zhen Dong; Lu, Xiu Min 5 2003 Generalized difference methods and numerical simulation for unsaturated soil water flow problems. Zbl 1495.76076 Li, Huan Rong; Luo, Zhen Dong; Xie, Zheng Hui; Zhu, Jiang 5 2006 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 The Crank-Nicolson finite spectral element method and numerical simulations for 2D non-stationary Navier-Stokes equations. Zbl 1452.65278 Luo, Zhendong; Jiang, Wenrui 5 2020 A natural boundary element method for the Sobolev equation in the 2D unbounded domain. Zbl 1422.65431 Teng, Fei; Luo, Zhendong; Yang, Jing 4 2017 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 4 2015 A new finite volume element formulation for the non-stationary Navier-Stokes equations. Zbl 1310.65102 Luo, Zhendong 4 2014 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 4 2004 A reduced-order extrapolating space-time continuous finite element method for the 2D Sobolev equation. Zbl 07777656 Yang, Jing; Luo, Zhendong 4 2020 The reduced-order method of continuous space-time finite element scheme for the non-stationary incompressible flows. Zbl 07518115 Luo, Zhendong; Yang, Jing 4 2022 The mixed finite element method for the non stationary conduction-convection problems. Zbl 0919.76050 Luo, Zhendong 3 1998 The third order estimate of mixed finite element for the Navier-Stokes problem. Zbl 0967.76558 Luo, Zhendong 3 1995 A Crank-Nicolson finite difference scheme for the Riesz space fractional-order parabolic-type sine-Gordon equation. Zbl 1446.65086 Zhou, Yanjie; Luo, Zhendong 3 2018 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 Self-discrete finite volume element simulation for a two-dimension unsaturated soil water flow problem. Zbl 1240.76012 Li, Huanrong; Luo, Zhendong 3 2011 A collocation spectral method for two-dimensional Sobolev equations. Zbl 1499.65560 Jin, Shiju; Luo, Zhendong 3 2018 Bubble stabilization and a posteriori error estimate of MFE method for plane elasticity problems. Zbl 1115.74051 Luo, Zhendong 3 2006 A nonlinear Galerkin mixed element method and a posteriori error estimator for the stationary Navier-Stokes equations. Zbl 1143.76481 Luo, Zhendong; Zhu, Jiang 3 2002 An optimized FD extrapolated scheme based on POD for the 2D integro-differential equation of parabolic type. Zbl 1454.65132 Luo, Zhendong 3 2020 A reduced-order extrapolation algorithm of fully second-order finite difference scheme for non-stationary Burgers equation. Zbl 1488.65288 Sun, Ping; Li, Hong; Teng, Fei; Luo, Zhendong 3 2012 Nonlinear Galerkin mixed element methods for the non-stationary conduction-convection problems. I: The continuous-time case. Zbl 0928.76059 Luo, Zhendong; Wang, Lieheng 2 1998 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 The reduced-order method of continuous space-time finite element scheme for the non-stationary incompressible flows. Zbl 07518115 Luo, Zhendong; Yang, Jing 4 2022 The reduced-dimension technique for the unknown solution coefficient vectors in the Crank-Nicolson finite element method for the Sobolev equation. Zbl 1490.65216 Zeng, Yihui; Luo, Zhendong 2 2022 A reduced-order extrapolated finite difference iterative scheme for uniform transmission line equation. Zbl 1484.65178 Deng, Qiuxiang; Luo, Zhendong 1 2022 A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation. Zbl 1458.35381 Zhou, Yanjie; Zhang, Yanan; Liang, Ye; Luo, Zhendong 8 2021 A reduced-order extrapolated approach to solution coefficient vectors in the Crank-Nicolson finite element method for the uniform transmission line equation. Zbl 1452.65250 Teng, Fei; Luo, Zhendong 2 2021 A highly efficient reduced-order extrapolating model for the 2D viscoelastic wave equation. Zbl 1488.65390 Teng, Fei; Luo, Zhendong 1 2021 A highly efficient reduced-order extrapolated finite difference algorithm for time-space tempered fractional diffusion-wave equation. Zbl 1440.65093 Luo, Zhendong; Wang, Hui 22 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 16 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 15 2020 A reduced-order extrapolated finite difference iterative method for the Riemann-Liouville tempered fractional derivative equation. Zbl 1446.65073 Luo, Zhendong; Ren, Hulin 15 2020 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 13 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 11 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 5 2020 A reduced-order extrapolating space-time continuous finite element method for the 2D Sobolev equation. Zbl 07777656 Yang, Jing; Luo, Zhendong 4 2020 An optimized FD extrapolated scheme based on POD for the 2D integro-differential equation of parabolic type. Zbl 1454.65132 Luo, Zhendong 3 2020 A reduced order extrapolating technique of solution coefficient vectors to collocation spectral method for telegraph equation. Zbl 1487.65190 Wang, Hui; He, Qingfang; Luo, Zhendong 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 58 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 22 2019 Proper orthogonal decomposition methods for partial differential equations. Zbl 1458.65002 Luo, Zhendong; Chen, Goong 6 2019 A Crank-Nicolson collocation spectral method for the two-dimensional viscoelastic wave equation. Zbl 1418.76037 Jin, Shiju; Luo, Zhendong 5 2019 A reduced-order extrapolated natural boundary element method based on POD for the parabolic equation in the 2D unbounded domain. Zbl 1438.65309 Teng, Fei; Luo, Zhen Dong; Yang, Jing 5 2019 A reduced-order extrapolating collocation spectral method based on POD for the 2D Sobolev equations. Zbl 1513.65409 Jin, Shiju; Luo, Zhendong 5 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 2 2019 A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation. Zbl 1427.65174 Luo, Zhendong; Teng, Fei 16 2018 A POD-based reduced-order Crank-Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations. Zbl 1484.65193 Luo, Zhendong; Teng, Fei; Chen, Jing 9 2018 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 6 2018 A Crank-Nicolson collocation spectral method for the two-dimensional telegraph equations. Zbl 1498.65181 Zhou, Yanjie; Luo, Zhendong 6 2018 A Crank-Nicolson finite difference scheme for the Riesz space fractional-order parabolic-type sine-Gordon equation. Zbl 1446.65086 Zhou, Yanjie; Luo, Zhendong 3 2018 A collocation spectral method for two-dimensional Sobolev equations. Zbl 1499.65560 Jin, Shiju; Luo, Zhendong 3 2018 A Crank-Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity-stream functions. Zbl 1498.65209 Zhou, Yanjie; Luo, Zhendong; Teng, Fei 2 2018 An optimized SPDMFE extrapolation approach based on the POD technique for 2D viscoelastic wave equation. Zbl 1353.74078 Luo, Zhendong; Teng, Fei 12 2017 Analysis of a space-time continuous Galerkin method for convection-dominated Sobolev equations. Zbl 1372.65277 Zhao, Zhihui; Li, Hong; Luo, Zhendong 8 2017 A reduced-order extrapolation spectral-finite difference scheme based on the POD method for 2D second-order hyperbolic equations. Zbl 1488.65265 Luo, Zhendong; Jin, Shiju 8 2017 Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation. Zbl 1380.65190 Xia, Hong; Luo, Zhendong 7 2017 Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations. Zbl 1422.65211 Luo, Zhendong; Teng, Fei 7 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 7 2017 A space-time continuous Galerkin method with mesh modification for viscoelastic wave equations. Zbl 1373.65074 Zhao, Zhihui; Li, Hong; Luo, Zhendong 5 2017 An optimized finite difference Crank-Nicolson iterative scheme for the 2D Sobolev equation. Zbl 1422.65191 Xia, Hong; Luo, Zhendong 5 2017 A natural boundary element method for the Sobolev equation in the 2D unbounded domain. Zbl 1422.65431 Teng, Fei; Luo, Zhendong; Yang, Jing 4 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 2 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 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 16 2016 A new space-time continuous Galerkin method with mesh modification for Sobolev equations. Zbl 1382.65335 Zhao, Zhihui; Li, Hong; Luo, Zhendong 15 2016 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 13 2016 A space-time continuous finite element method for 2D viscoelastic wave equation. Zbl 1332.74047 Li, Hong; Zhao, Zhihui; Luo, Zhendong 10 2016 A stabilized Crank-Nicolson mixed finite volume element formulation for the non-stationary incompressible Boussinesq equations. Zbl 1332.65127 Luo, Zhen Dong 8 2016 A stabilized mixed finite element formulation for the non-stationary incompressible Boussinesq equations. Zbl 1363.76042 Luo, Zhendong 6 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 5 2016 A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations. Zbl 1344.65088 Luo, Zhendong 2 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 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 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 18 2015 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 11 2015 A POD-based reduced-order stabilized Crank-Nicolson MFE formulation for the non-stationary parabolized Navier-Stokes equations. Zbl 1488.65444 Luo, Zhendong 10 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 9 2015 A POD-based reduced-order TSCFE extrapolation iterative format for two-dimensional heat equations. Zbl 1411.74060 Luo, Zhendong 7 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 5 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 4 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 11 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 9 2014 A reduced-order extrapolation algorithm based on SFVE method and POD technique for non-stationary Stokes equations. Zbl 1338.76077 Luo, Zhendong 6 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 5 2014 A POD reduced-order SPDMFE extrapolating algorithm for hyperbolic equations. Zbl 1313.65267 Luo, Zhendong; Li, Hong 5 2014 A POD-based reduced-order FD extrapolating algorithm for traffic flow. Zbl 1343.76032 Luo, Zhendong; Xie, Di; Teng, Fei 5 2014 A POD-based reduced-order finite difference extrapolating model with fully second-order accuracy for non-stationary Stokes equations. Zbl 1507.65142 Luo, Zhendong; Teng, Fei; Di, Zhenhua 5 2014 A new finite volume element formulation for the non-stationary Navier-Stokes equations. Zbl 1310.65102 Luo, Zhendong 4 2014 A POD-based reduced-order CN finite element extrapolating model for unsaturated soil water flow equation. Zbl 1313.76064 Teng, Fei; Luo, Zhendong 2 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 23 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 14 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 13 2013 A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems. Zbl 1490.65171 Luo, Zhendong; Li, Hong; Sun, Ping; An, Jing; Navon, Ionel Michael 8 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 new splitting positive definite mixed finite element method for a viscoelastic equation. Zbl 1495.65171 Li, Xian Chong; Sun, Ping; An, Jing; Luo, Zhen Dong 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 35 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 21 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 10 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 7 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. 7 2012 A reduced-order extrapolation algorithm of fully second-order finite difference scheme for non-stationary Burgers equation. Zbl 1488.65288 Sun, Ping; Li, Hong; Teng, Fei; Luo, Zhendong 3 2012 A reduced FE formulation based on POD method for hyperbolic equations. Zbl 1274.65273 Luo, Zhendong; Ou, Qiulan; Wu, Jiarong; Xie, Zhenghui 2 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 fully discrete finite volume element formulation and numerical simulations for viscoelastic equations. Zbl 1289.74161 Li, Hong; Sun, Ping; Shang, Yueqiang; Luo, Zhendong 1 2012 A reduced-order finite volume element formulation based on POD method and implementation of its extrapolation algorithm for unsaturated soil water flow equation. Zbl 1488.65352 Luo, Zhendong; Li, Hong; Chen, Jing 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 38 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 24 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 18 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 18 2011 Numerical simulation based on POD for two-dimensional solute transport problems. Zbl 1217.74082 Li, Huanrong; Luo, Zhendong; Chen, Jing 18 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. 17 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 11 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 A reduced second-order time accurate finite element formulation based on POD for parabolic equations. Zbl 1488.65445 Luo, Zhendong; Chen, Jing; Xie, Zhenghui; An, Jing; Sun, Ping 6 2011 Self-discrete finite volume element simulation for a two-dimension unsaturated soil water flow problem. Zbl 1240.76012 Li, Huanrong; Luo, Zhendong 3 2011 ...and 36 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 688 Authors 82 Luo, Zhendong 31 Li, Hong 22 Navon, Ionel Michael 21 Dehghan Takht Fooladi, Mehdi 20 Abbaszadeh, Mostafa 16 Liu, Yang 16 Teng, Fei 15 Li, Huanrong 14 Fang, Fangxin 12 Iliescu, Traian 12 Pain, Christopher C. 11 Huang, Pengzhan 11 Shang, Yueqiang 11 Si, Zhiyong 11 Zhou, Yanjie 9 He, Yinnian 8 Zhu, Jiang 7 Chen, Jing 7 Fang, Zhichao 7 Hou, Yanren 7 Shi, Dongyang 7 Sun, Ping 7 Wang, Jinfeng 7 Wang, Zhu 7 Xie, Zhenghui 7 Zhang, Tong 6 Buchan, Andrew G. 6 Feng, Xinlong 6 Rui, Hongxing 6 Song, Zhengyuan 6 Xia, Hong 6 Zhao, Zhihui 5 An, Jing 5 Chen, Huanzhen 5 Gao, Junqiang 5 Huang, Ting-Zhu 5 Lanteri, Stéphane 5 Li, Kun 5 Li, Liang 5 Song, Junpeng 5 Zhang, Yunzhang 4 Chen, Chuanjun 4 Du, Juan 4 He, Siriguleng 4 Jin, Shiju 4 Li, Qing 4 Wang, Dongmei 4 Xiao, Dunhui 4 Xie, Xiaoping 4 Zhang, Xiaohua 4 Zhao, Jie 3 Allison, P. A. 3 Borggaard, Jeff T. 3 Chen, Xiao 3 Chu, Xiaochen 3 Di, Zhenhua 3 Durlofsky, Louis J. 3 Gao, Wei 3 Ghaffari, Rezvan 3 Ghoreishi, Farideh 3 Goddard, A. J. H. 3 Gorman, Gerard J. 3 Heemink, Arnold Willem 3 Huang, Qiumei 3 Kumar, Naresh 3 Li, Jian 3 Liu, Qian 3 Nikan, Omid 3 Piggott, Matthew D. 3 Qin, Jin 3 Ramos, Juan I. 3 Rebholz, Leo G. 3 Ruiz-Baier, Ricardo 3 Singler, John R. 3 Soulaimani, Azzeddine 3 Xu, Fei 3 Yang, Jing 3 Yang, Xiaozhong 3 Yu, Jian 3 Zada, Akbar 3 Zeng, Yihui 3 Zhao, Wenju 3 Zokagoa, Jean Marie 2 Akhtar, Imran 2 Allery, Cyrille 2 Altaf, M. Umer 2 Alzabut, Jehad O. 2 Ammar, Amine 2 Avazzadeh, Zakieh 2 Băleanu, Dumitru I. 2 Bi, Hai 2 Biegler, Lorenz T. 2 Cao, Yanhua 2 Cardoso, M. 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Mathematics 1 International Journal for Numerical Methods in Biomedical Engineering 1 Journal of Applied Mathematics & Informatics 1 Journal of Applied Analysis and Computation 1 Mathematical Sciences 1 Journal of Function Spaces 1 Computational Methods for Differential Equations 1 Open Mathematics 1 Applied Mathematics and Nonlinear Sciences ...and 2 more Serials all top 5 Cited in 39 Fields 358 Numerical analysis (65-XX) 195 Partial differential equations (35-XX) 171 Fluid mechanics (76-XX) 31 Ordinary differential equations (34-XX) 30 Mechanics of deformable solids (74-XX) 25 Geophysics (86-XX) 14 Real functions (26-XX) 13 Biology and other natural sciences (92-XX) 12 Optics, electromagnetic theory (78-XX) 12 Systems theory; control (93-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Probability theory and stochastic processes (60-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Statistics (62-XX) 5 Computer science (68-XX) 5 Operations research, mathematical programming (90-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Approximations and expansions (41-XX) 3 Integral equations (45-XX) 3 Operator theory (47-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Special functions (33-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Information and communication theory, circuits (94-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX) Citations by Year