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## Zhou, Aihui

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 Author ID: zhou.aihui Published as: Zhou, Aihui; Zhou, A.; Zhou, Ai-hui; Zhou, Ai Hui
 Documents Indexed: 133 Publications since 1984, including 3 Books
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#### Co-Authors

 17 single-authored 22 Ding, Jiu 11 Dai, Xiaoying 11 Lin, Qun 10 Chen, Huajie 9 Gong, Xingao 9 Liu, Fang 8 Xu, Jinchao 7 He, Lianhua 7 Shen, Lihua 6 Gao, Xingyu 4 Allegretto, Walter 4 Fang, Jun 4 Lin, Yanping 4 Ma, Xiuling 4 Yan, Ningning 4 Zhang, Dier 3 Mao, Dong 3 Shih, Tsimin 3 Stynes, Martin 3 Xin, Jack X. 3 Yang, Ying 3 Yang, Zhang 2 Gu, Hong 2 He, Yinnian 2 Huang, Hung-Tsai 2 Jin, Congming 2 Li, Zi-Cai 2 Liang, Shengde 2 Lu, Tao 2 Xu, Yuesheng 2 Zhou, Yunkai 1 Bao, Gang 1 Chelikowsky, James R. 1 Chen, Zhongying 1 Franz, Sebastian 1 Kuang, Xiong 1 Li, Jian 1 Li, Jichun 1 Li, Ronghua 1 Li, Tien-Yien 1 Liao, Xiaohai 1 Liem, Chinbo 1 Liu, Zhuang 1 Lü, Lao 1 Madden, Niall 1 Naga, Ahmed 1 Pan, Jianhua 1 Pflaum, Christoph 1 Reich, Nils 1 Ren, Zhongdao 1 Rhee, Noah H. 1 Roos, Hans-Görg 1 Rüde, Ulrich 1 Schneider, Reinhold 1 Shu, Shi 1 Sun, Jiguang 1 Tobiska, Lutz 1 Wang, Qiao 1 Wang, Zheng 1 Wen, Zaiwen 1 Winter, Christoph 1 Yang, Bin 1 Zhang, Liwei 1 Zhang, Zhimin 1 Zhou, Yuzhi 1 Zhu, Jinwei
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#### Serials

 8 Journal of Computational Mathematics 7 Advances in Computational Mathematics 6 Systems Science and Mathematical Sciences 5 Computer Methods in Applied Mechanics and Engineering 5 Numerische Mathematik 5 SIAM Journal on Scientific Computing 4 Applied Mathematics and Computation 4 SIAM Journal on Numerical Analysis 4 Journal of Scientific Computing 4 Acta Mathematica Scientia 4 Multiscale Modeling & Simulation 3 IMA Journal of Numerical Analysis 3 Journal of Statistical Physics 3 Mathematical Methods in the Applied Sciences 3 BIT 3 Journal of Computational and Applied Mathematics 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Natural Science Journal of Xiangtan University 3 Science China. Mathematics 2 Journal of Computational Physics 2 Nonlinearity 2 Mathematics of Computation 2 Applied Mathematics Letters 2 Journal of Integral Equations and Applications 2 International Journal of Numerical Analysis and Modeling 2 Communications in Computational Physics 2 Nonlinear Analysis. Theory, Methods & Applications 1 Journal of Mathematical Analysis and Applications 1 Physics Letters. A 1 Advances in Mathematics 1 Journal of Engineering Mathematics (Xi’an) 1 Physica D 1 Applied Numerical Mathematics 1 Journal of Systems Science and Mathematical Sciences 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Acta Mathematicae Applicatae Sinica. English Series 1 Hunan Annals of Mathematics 1 Numerical Methods for Partial Differential Equations 1 Science in China. Series A 1 Applications of Mathematics 1 Journal of Partial Differential Equations 1 Electronic Journal of Differential Equations (EJDE) 1 Monte Carlo Methods and Applications 1 Discrete and Continuous Dynamical Systems 1 Journal of Mathematical Chemistry 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Journal of Systems Science and Complexity 1 Communications on Pure and Applied Analysis 1 HERMIS-$$\mu\pi$$. Hellenic European Research on Mathematics and Informatics Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Mathematical Modelling of Natural Phenomena 1 Numerical Mathematics: Theory, Methods and Applications 1 Advances in Applied Mathematics and Mechanics 1 Monographs and Research Notes in Mathematics
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#### Fields

 108 Numerical analysis (65-XX) 70 Partial differential equations (35-XX) 24 Quantum theory (81-XX) 14 Operator theory (47-XX) 13 Dynamical systems and ergodic theory (37-XX) 9 Integral equations (45-XX) 8 Fluid mechanics (76-XX) 8 Statistical mechanics, structure of matter (82-XX) 5 Measure and integration (28-XX) 5 Optics, electromagnetic theory (78-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Functional analysis (46-XX) 3 Operations research, mathematical programming (90-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

101 Publications have been cited 1,406 times in 808 Documents Cited by Year
A two-grid discretization scheme for eigenvalue problems. Zbl 0959.65119
Xu, Jinchao; Zhou, Aihui
2001
Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation. Zbl 1068.65122
Lin, Qun; Tobiska, Lutz; Zhou, Aihui
2005
Local and parallel finite element algorithms based on two-grid discretizations. Zbl 0948.65122
Xu, Jinchao; Zhou, Aihui
2000
Convergence and optimal complexity of adaptive finite element eigenvalue computations. Zbl 1159.65090
Dai, Xiaoying; Xu, Jinchao; Zhou, Aihui
2008
Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems. Zbl 0990.65128
Xu, Jinchao; Zhou, Aihui
2001
Local and parallel finite element algorithms for the Stokes problem. Zbl 1145.65097
He, Yinnian; Xu, Jinchao; Zhou, Aihui; Li, Jian
2008
Local and parallel finite element algorithms for the Navier-Stokes problem. Zbl 1093.76035
He, Yinnian; Xu, Jinchao; Zhou, Aihui
2006
Local and parallel finite element algorithms for eigenvalue problems. Zbl 1015.65060
Xu, Jinchao; Zhou, Aihui
2002
Eigenvalues of rank-one updated matrices with some applications. Zbl 1139.15003
Ding, Jiu; Zhou, Aihui
2007
A note on the optimal $$L^2$$-estimate of the finite volume element method. Zbl 0997.65122
Chen, Zhongying; Li, Ronghua; Zhou, Aihui
2002
Three-scale finite element discretizations for quantum eigenvalue problems. Zbl 1160.65060
Dai, Xiaoying; Zhou, Aihui
2008
Finite approximations of Frobenius-Perron operators. A solution of Ulam’s conjecture to multi-dimensional transformations. Zbl 0890.58035
Ding, Jiu; Zhou, Aihui
1996
Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes. Zbl 0986.65098
Yan, Ningning; Zhou, Aihui
2001
Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates. Zbl 1103.65112
Mao, Dong; Shen, Lihua; Zhou, Aihui
2006
A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions. Zbl 1188.65153
Liu, Fang; Madden, Niall; Stynes, Martin; Zhou, Aihui
2009
Symmetric finite volume discretizations for parabolic problems. Zbl 1038.65079
Ma, Xiuling; Shu, Shi; Zhou, Aihui
2003
Enhancing eigenvalue approximation by gradient recovery. Zbl 1148.65087
Naga, Ahmed; Zhang, Zhimin; Zhou, Aihui
2006
Finite element approximations of nonlinear eigenvalue problems in quantum physics. Zbl 1228.81026
Chen, Huajie; He, Lianhua; Zhou, Aihui
2011
The full approximation accuracy for the stream function-vorticity- pressure method. Zbl 0823.65110
Zhou, Aihui; Li, Jichun
1994
Adaptive finite element approximations for Kohn-Sham models. Zbl 1316.35260
Chen, Huajie; Dai, Xiaoying; Gong, Xingao; He, Lianhua; Zhou, Aihui
2014
Piecewise linear Markov approximations of Frobenius-Perron operators associated with multi-dimensional transformations. Zbl 0907.47025
Ding, Jiu; Zhou, Ai Hui
1995
Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh. Zbl 1221.81225
Zhang, Dier; Shen, Lihua; Zhou, Aihui; Gong, Xin-Gao
2008
Numerical analysis of finite dimensional approximations of Kohn-Sham models. Zbl 1278.35225
Chen, Huajie; Gong, Xingao; He, Lianhua; Yang, Zhang; Zhou, Aihui
2013
An analysis of finite-dimensional approximations for the ground state solution of Bose-Einstein condensates. Zbl 1051.35094
Zhou, Aihui
2004
Error analysis of the combination technique. Zbl 0942.65122
Pflaum, C.; Zhou, A.
1999
Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model. Zbl 1194.35293
Chen, Huajie; Gong, Xingao; Zhou, Aihui
2010
A box scheme for coupled systems resulting from microsensor thermistor problems. Zbl 0979.78023
Allegretto, Walter; Lin, Yanping; Zhou, Aihui
1999
A defect correction scheme for finite element eigenvalues with applications to quantum Chemistry. Zbl 1104.65323
Shen, Lihua; Zhou, Aihui
2006
Statistical properties of deterministic systems. Zbl 1171.37001
Ding, Jiu; Zhou, Aihui
2009
Multi-parameter extrapolation methods for boundary integral equations. Zbl 0922.65075
Rüde, Ulrich; Zhou, Aihui
1998
The projection method for computing multidimensional absolutely continuous invariant measures. Zbl 0972.28501
Ding, Jiu; Zhou, Aihui
1994
Finite element approximations for Schrödinger equations with applications to electronic structure computations. Zbl 1174.65047
Gong, Xingao; Shen, Lihua; Zhang, Dier; Zhou, Aihui
2008
Nonnegative matrices, positive operators, and applications. Zbl 1205.15048
Ding, Jiu; Zhou, Aihui
2009
Convergence and quasi-optimal complexity of adaptive finite element computations for multiple eigenvalues. Zbl 1332.65159
Dai, Xiaoying; He, Lianhua; Zhou, Aihui
2015
Gradient type optimization methods for electronic structure calculations. Zbl 1300.82006
Zhang, Xin; Zhu, Jinwei; Wen, Zaiwen; Zhou, Aihui
2014
A symmetric finite volume scheme for selfadjoint elliptic problems. Zbl 1027.65150
Liang, Shengde; Ma, Xiuling; Zhou, Aihui
2002
Finite element methods for eigenvalue problems. Zbl 1351.65085
Sun, Jiguang; Zhou, Aihui
2017
A multi-parameter splitting extrapolation and a parallel algorithm. Zbl 0895.65058
Zhou, Aihui; Liem, Chin-bo; Shih, Tsi-min; Lü, Tao
1997
Finite dimensional approximations for the electronic ground state solution of a molecular system. Zbl 1119.35095
Zhou, Aihui
2007
Orbital-free density functional theory for molecular structure calculations. Zbl 1174.81316
Chen, Huajie; Zhou, Aihui
2008
Convergence and complexity of adaptive finite element methods for elliptic partial differential equations. Zbl 1263.65103
He, Lianhua; Zhou, Aihui
2011
Finite approximations of Markov operators. Zbl 1013.65140
Ding, Jiu; Li, Tien Yien; Zhou, Aihui
2002
A Kohn-Sham equation solver based on hexahedral finite elements. Zbl 1245.82007
Fang, Jun; Gao, Xingyu; Zhou, Aihui
2012
Fast Boolean approximation methods for solving integral equations in high dimensions. Zbl 1085.65126
Xu, Yuesheng; Zhou, Aihui
2004
A maximum entropy method based on piecewise linear functions for the recovery of a stationary density of interval mappings. Zbl 1231.37042
Ding, Jiu; Jin, Congming; Rhee, Noah H.; Zhou, Aihui
2011
Multi-level adaptive corrections in finite dimensional approximations. Zbl 1224.65294
Zhou, Aihui
2010
Adaptive finite element approximations for a class of nonlinear eigenvalue problems in quantum physics. Zbl 1262.35187
Chen, Huajie; Gong, Xingao; He, Lianhua; Zhou, Aihui
2011
Optimal and superconvergence estimates of the finite element method for a scalar hyperbolic equation. Zbl 0805.65099
Zhou, Aihui; Lin, Qun
1994
Two-scale Boolean Galerkin discretizations for Fredholm integral equations of the second kind. Zbl 1144.65087
Liu, Fang; Zhou, Aihui
2007
A sparse finite element method with high accuracy. I. Zbl 0989.65134
Lin, Qun; Yan, Ningning; Zhou, Aihui
2001
An analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1099.65116
Schneider, Reinhold; Xu, Yuesheng; Zhou, Aihui
2006
Three-scale finite element eigenvalue discretizations. Zbl 1157.65061
Gao, X.; Liu, F.; Zhou, A.
2008
Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions. Zbl 1167.65064
Dai, Xiaoying; Yang, Zhang; Zhou, Aihui
2008
Characteristic polynomials of some perturbed matrices. Zbl 1154.15011
Ding, Jiu; Zhou, Aihui
2008
An analysis of some high accuracy finite element methods for hyperbolic problems. Zbl 1004.65100
Zhou, Aihui
2001
A multi-parameter splitting extrapolation and a parallel algorithm for elliptic eigenvalue problem. Zbl 0905.65106
Liao, Xiaohai; Zhou, Aihui
1998
Long-time stability of finite element approximations for parabolic equations with memory. Zbl 0931.65136
Allegretto, Walter; Lin, Yanping; Zhou, Aihui
1999
Error analysis on bi-parameter finite elements. Zbl 0945.65122
Zhou, Aihui; Liem, Chinbo; Shih, Tsimin; Lü, Lao
1998
Finite volume discretizations for eigenvalue problems with applications to electronic structure calculations. Zbl 1233.65082
Dai, Xiaoying; Gong, Xingao; Yang, Zhang; Zhang, Dier; Zhou, Aihui
2011
A two-scale higher-order finite element discretization for Schrödinger equation. Zbl 1212.65432
Chen, Huajie; Liu, Fang; Zhou, Aihui
2009
Hohenberg-Kohn theorem for Coulomb type systems and its generalization. Zbl 1308.81197
Zhou, Aihui
2012
Structure preserving finite element approximations of Markov operators. Zbl 1073.37091
Ding, Jiu; Zhou, Aihui
2002
Constructive approximations of Markov operators. Zbl 0991.37004
Ding, Jiu; Zhou, Aihui
2001
A local computational scheme for higher order finite element value approximation. Zbl 1168.65065
Dai, Xiaoying; Shen, Lihua; Zhou, Aihui
2008
Finite volume methods for eigenvalue problems. Zbl 0983.65124
Liang, Shengde; Ma, Xiuling; Zhou, Aihui
2001
New error estimates of biquadratic Lagrange elements for Poisson’s equation. Zbl 1091.65111
Huang, Hung-Tsai; Li, Zi-Cai; Zhou, Aihui
2006
Two-scale finite element discretizations for partial differential equations. Zbl 1100.65101
Liu, Fang; Zhou, Aihui
2006
A spectrum theorem for perturbed bounded linear operators. Zbl 1161.47004
Ding, Jiu; Zhou, Aihui
2008
The combination technique for a two-dimensional convection-diffusion problem with exponential layers. Zbl 1212.65443
Franz, Sebastian; Liu, Fang; Roos, Hans-Görg; Stynes, Martin; Zhou, Aihui
2009
Localizations and parallelizations for two-scale finite element discretizations. Zbl 1141.65079
Liu, Fang; Zhou, Aihui
2007
Notes on superconvergence and its related topics. Zbl 0790.65095
Lin, Qun; Zhou, Aihui
1993
Analysis of finite dimensional approximations to a class of partial differential equations. Zbl 1064.65125
Bao, Gang; Zhou, Aihui
2004
Extrapolation for finite volume approximations. Zbl 1036.65091
Ma, Xiuling; Mao, Dong; Zhou, Aihui
2003
Parallel mesh refinement of higher order finite elements for electronic structure calculations. Zbl 1364.65259
Zhang, Dier; Zhou, Aihui; Gong, Xin-Gao
2008
Global superconvergence approximations of the mixed finite element method for the Stokes problem and the linear elasticity equation. Zbl 0858.73076
Zhou, Aihui
1996
Local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation. Zbl 1121.65367
Yang, Ying; Zhou, Aihui
2006
A finite element recovery approach to eigenvalue approximations with applications to electronic structure calculations. Zbl 1272.65086
Fang, Jun; Gao, Xingyu; Zhou, Aihui
2013
Finite element computation of KPP front speeds in 3D cellular and ABC flows. Zbl 1416.65465
Shen, L.; Xin, J.; Zhou, A.
2013
Defect correction for finite element gradient. Zbl 0767.65001
Lin, Qun; Zhou, Aihui
1992
Extrapolation for collocation method of the first kind Volterra integral equations. Zbl 0755.65138
Zhou, Aihui
1991
Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem. Zbl 0917.76042
Zhou, Aihui
1999
A finite element method for the Frobenius-Perron operator equation. Zbl 0977.65104
Ding, Jiu; Zhou, Aihui
1999
Multi-parameter error resolution for the collocation method of Volterra integral equations. Zbl 0910.65110
Zhou, Aihui
1997
The projection method for a class of Frobenius-Perron operators. Zbl 0943.47042
Ding, J.; Zhou, A.
1999
On the “preconditioning” function used in planewave DFT calculations and its generalization. Zbl 1388.65195
Zhou, Yunkai; Chelikowsky, James R.; Gao, Xingyu; Zhou, Aihui
2015
Interpolation based local postprocessing for adaptive finite element approximations in electronic structure calculations. Zbl 1218.81044
Fang, Jun; Gao, Xingyu; Gong, Xingao; Zhou, Aihui
2011
Convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. Zbl 0787.65071
Lin, Qun; Zhou, Aihui
1993
Two-scale finite element discretizations for integrodifferential equations. Zbl 1238.65125
Chen, Huajie; Liu, Fang; Reich, Nils; Winter, Christoph; Zhou, Aihui
2011
Finite element computation of KPP front speeds in cellular and cat’s eye flows. Zbl 1366.76055
Shen, Lihua; Xin, Jack; Zhou, Aihui
2013
A singularity-based eigenfunction decomposition for Kohn-Sham equations. Zbl 1386.35316
Zhang, Xin; Zhou, Aihui
2016
Postprocessed two-scale finite element discretizations. I. Zbl 1241.65101
Liu, Fang; Stynes, Martin; Zhou, Aihui
2011
Parallel computation and domain decomposition for a class of hyperbolic problems. Zbl 0842.65070
Lin, Qun; Yan, Ningning; Zhou, Aihui
1995
On estimating absolutely continuous invariant measures. Zbl 1031.37004
Ding, Jiu; Zhou, Aihui
2001
An extrapolation method for finite element approximation of integro- differential equations with parameters. Zbl 0734.65098
Zhou, Aihui
1990
Absolutely continuous invariant measures for piecewise $$C^2$$ and expanding mappings in higher dimensions. Zbl 1009.37012
Ding, Jiu; Zhou, Aihui
2000
Invariant measures and their computation. Zbl 1054.37500
Ding, Jiu; Zhou, Aihui
1998
A conjugate gradient method for electronic structure calculations. Zbl 1378.65120
Dai, Xiaoying; Liu, Zhuang; Zhang, Liwei; Zhou, Aihui
2017
A posteriori error estimates for Markov approximations of Frobenius-Perron operators. Zbl 1119.41018
Ding, Jiu; Jin, Congming; Zhou, Aihui
2007
A finite element recovery approach to Green’s function approximations with applications to electrostatic potential computation. Zbl 1157.78002
Yang, Ying; Zhou, Aihui
2009
Finite element computations of Kolmogorov-Petrovsky-Piskunov front speeds in random shear flows in cylinders. Zbl 1400.76096
Shen, Lihua; Xin, Jack; Zhou, Aihui
2008
A mathematical aspect of Hohenberg-Kohn theorem. Zbl 1409.81189
Zhou, Aihui
2019
Finite element methods for eigenvalue problems. Zbl 1351.65085
Sun, Jiguang; Zhou, Aihui
2017
A conjugate gradient method for electronic structure calculations. Zbl 1378.65120
Dai, Xiaoying; Liu, Zhuang; Zhang, Liwei; Zhou, Aihui
2017
A singularity-based eigenfunction decomposition for Kohn-Sham equations. Zbl 1386.35316
Zhang, Xin; Zhou, Aihui
2016
Convergence and quasi-optimal complexity of adaptive finite element computations for multiple eigenvalues. Zbl 1332.65159
Dai, Xiaoying; He, Lianhua; Zhou, Aihui
2015
On the “preconditioning” function used in planewave DFT calculations and its generalization. Zbl 1388.65195
Zhou, Yunkai; Chelikowsky, James R.; Gao, Xingyu; Zhou, Aihui
2015
Adaptive finite element approximations for Kohn-Sham models. Zbl 1316.35260
Chen, Huajie; Dai, Xiaoying; Gong, Xingao; He, Lianhua; Zhou, Aihui
2014
Gradient type optimization methods for electronic structure calculations. Zbl 1300.82006
Zhang, Xin; Zhu, Jinwei; Wen, Zaiwen; Zhou, Aihui
2014
Numerical analysis of finite dimensional approximations of Kohn-Sham models. Zbl 1278.35225
Chen, Huajie; Gong, Xingao; He, Lianhua; Yang, Zhang; Zhou, Aihui
2013
A finite element recovery approach to eigenvalue approximations with applications to electronic structure calculations. Zbl 1272.65086
Fang, Jun; Gao, Xingyu; Zhou, Aihui
2013
Finite element computation of KPP front speeds in 3D cellular and ABC flows. Zbl 1416.65465
Shen, L.; Xin, J.; Zhou, A.
2013
Finite element computation of KPP front speeds in cellular and cat’s eye flows. Zbl 1366.76055
Shen, Lihua; Xin, Jack; Zhou, Aihui
2013
A Kohn-Sham equation solver based on hexahedral finite elements. Zbl 1245.82007
Fang, Jun; Gao, Xingyu; Zhou, Aihui
2012
Hohenberg-Kohn theorem for Coulomb type systems and its generalization. Zbl 1308.81197
Zhou, Aihui
2012
Finite element approximations of nonlinear eigenvalue problems in quantum physics. Zbl 1228.81026
Chen, Huajie; He, Lianhua; Zhou, Aihui
2011
Convergence and complexity of adaptive finite element methods for elliptic partial differential equations. Zbl 1263.65103
He, Lianhua; Zhou, Aihui
2011
A maximum entropy method based on piecewise linear functions for the recovery of a stationary density of interval mappings. Zbl 1231.37042
Ding, Jiu; Jin, Congming; Rhee, Noah H.; Zhou, Aihui
2011
Adaptive finite element approximations for a class of nonlinear eigenvalue problems in quantum physics. Zbl 1262.35187
Chen, Huajie; Gong, Xingao; He, Lianhua; Zhou, Aihui
2011
Finite volume discretizations for eigenvalue problems with applications to electronic structure calculations. Zbl 1233.65082
Dai, Xiaoying; Gong, Xingao; Yang, Zhang; Zhang, Dier; Zhou, Aihui
2011
Interpolation based local postprocessing for adaptive finite element approximations in electronic structure calculations. Zbl 1218.81044
Fang, Jun; Gao, Xingyu; Gong, Xingao; Zhou, Aihui
2011
Two-scale finite element discretizations for integrodifferential equations. Zbl 1238.65125
Chen, Huajie; Liu, Fang; Reich, Nils; Winter, Christoph; Zhou, Aihui
2011
Postprocessed two-scale finite element discretizations. I. Zbl 1241.65101
Liu, Fang; Stynes, Martin; Zhou, Aihui
2011
Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model. Zbl 1194.35293
Chen, Huajie; Gong, Xingao; Zhou, Aihui
2010
Multi-level adaptive corrections in finite dimensional approximations. Zbl 1224.65294
Zhou, Aihui
2010
A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions. Zbl 1188.65153
Liu, Fang; Madden, Niall; Stynes, Martin; Zhou, Aihui
2009
Statistical properties of deterministic systems. Zbl 1171.37001
Ding, Jiu; Zhou, Aihui
2009
Nonnegative matrices, positive operators, and applications. Zbl 1205.15048
Ding, Jiu; Zhou, Aihui
2009
A two-scale higher-order finite element discretization for Schrödinger equation. Zbl 1212.65432
Chen, Huajie; Liu, Fang; Zhou, Aihui
2009
The combination technique for a two-dimensional convection-diffusion problem with exponential layers. Zbl 1212.65443
Franz, Sebastian; Liu, Fang; Roos, Hans-Görg; Stynes, Martin; Zhou, Aihui
2009
A finite element recovery approach to Green’s function approximations with applications to electrostatic potential computation. Zbl 1157.78002
Yang, Ying; Zhou, Aihui
2009
Convergence and optimal complexity of adaptive finite element eigenvalue computations. Zbl 1159.65090
Dai, Xiaoying; Xu, Jinchao; Zhou, Aihui
2008
Local and parallel finite element algorithms for the Stokes problem. Zbl 1145.65097
He, Yinnian; Xu, Jinchao; Zhou, Aihui; Li, Jian
2008
Three-scale finite element discretizations for quantum eigenvalue problems. Zbl 1160.65060
Dai, Xiaoying; Zhou, Aihui
2008
Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh. Zbl 1221.81225
Zhang, Dier; Shen, Lihua; Zhou, Aihui; Gong, Xin-Gao
2008
Finite element approximations for Schrödinger equations with applications to electronic structure computations. Zbl 1174.65047
Gong, Xingao; Shen, Lihua; Zhang, Dier; Zhou, Aihui
2008
Orbital-free density functional theory for molecular structure calculations. Zbl 1174.81316
Chen, Huajie; Zhou, Aihui
2008
Three-scale finite element eigenvalue discretizations. Zbl 1157.65061
Gao, X.; Liu, F.; Zhou, A.
2008
Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions. Zbl 1167.65064
Dai, Xiaoying; Yang, Zhang; Zhou, Aihui
2008
Characteristic polynomials of some perturbed matrices. Zbl 1154.15011
Ding, Jiu; Zhou, Aihui
2008
A local computational scheme for higher order finite element value approximation. Zbl 1168.65065
Dai, Xiaoying; Shen, Lihua; Zhou, Aihui
2008
A spectrum theorem for perturbed bounded linear operators. Zbl 1161.47004
Ding, Jiu; Zhou, Aihui
2008
Parallel mesh refinement of higher order finite elements for electronic structure calculations. Zbl 1364.65259
Zhang, Dier; Zhou, Aihui; Gong, Xin-Gao
2008
Finite element computations of Kolmogorov-Petrovsky-Piskunov front speeds in random shear flows in cylinders. Zbl 1400.76096
Shen, Lihua; Xin, Jack; Zhou, Aihui
2008
Eigenvalues of rank-one updated matrices with some applications. Zbl 1139.15003
Ding, Jiu; Zhou, Aihui
2007
Finite dimensional approximations for the electronic ground state solution of a molecular system. Zbl 1119.35095
Zhou, Aihui
2007
Two-scale Boolean Galerkin discretizations for Fredholm integral equations of the second kind. Zbl 1144.65087
Liu, Fang; Zhou, Aihui
2007
Localizations and parallelizations for two-scale finite element discretizations. Zbl 1141.65079
Liu, Fang; Zhou, Aihui
2007
A posteriori error estimates for Markov approximations of Frobenius-Perron operators. Zbl 1119.41018
Ding, Jiu; Jin, Congming; Zhou, Aihui
2007
Local and parallel finite element algorithms for the Navier-Stokes problem. Zbl 1093.76035
He, Yinnian; Xu, Jinchao; Zhou, Aihui
2006
Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates. Zbl 1103.65112
Mao, Dong; Shen, Lihua; Zhou, Aihui
2006
Enhancing eigenvalue approximation by gradient recovery. Zbl 1148.65087
Naga, Ahmed; Zhang, Zhimin; Zhou, Aihui
2006
A defect correction scheme for finite element eigenvalues with applications to quantum Chemistry. Zbl 1104.65323
Shen, Lihua; Zhou, Aihui
2006
An analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1099.65116
Schneider, Reinhold; Xu, Yuesheng; Zhou, Aihui
2006
New error estimates of biquadratic Lagrange elements for Poisson’s equation. Zbl 1091.65111
Huang, Hung-Tsai; Li, Zi-Cai; Zhou, Aihui
2006
Two-scale finite element discretizations for partial differential equations. Zbl 1100.65101
Liu, Fang; Zhou, Aihui
2006
Local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation. Zbl 1121.65367
Yang, Ying; Zhou, Aihui
2006
Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation. Zbl 1068.65122
Lin, Qun; Tobiska, Lutz; Zhou, Aihui
2005
An analysis of finite-dimensional approximations for the ground state solution of Bose-Einstein condensates. Zbl 1051.35094
Zhou, Aihui
2004
Fast Boolean approximation methods for solving integral equations in high dimensions. Zbl 1085.65126
Xu, Yuesheng; Zhou, Aihui
2004
Analysis of finite dimensional approximations to a class of partial differential equations. Zbl 1064.65125
Bao, Gang; Zhou, Aihui
2004
Symmetric finite volume discretizations for parabolic problems. Zbl 1038.65079
Ma, Xiuling; Shu, Shi; Zhou, Aihui
2003
Extrapolation for finite volume approximations. Zbl 1036.65091
Ma, Xiuling; Mao, Dong; Zhou, Aihui
2003
Local and parallel finite element algorithms for eigenvalue problems. Zbl 1015.65060
Xu, Jinchao; Zhou, Aihui
2002
A note on the optimal $$L^2$$-estimate of the finite volume element method. Zbl 0997.65122
Chen, Zhongying; Li, Ronghua; Zhou, Aihui
2002
A symmetric finite volume scheme for selfadjoint elliptic problems. Zbl 1027.65150
Liang, Shengde; Ma, Xiuling; Zhou, Aihui
2002
Finite approximations of Markov operators. Zbl 1013.65140
Ding, Jiu; Li, Tien Yien; Zhou, Aihui
2002
Structure preserving finite element approximations of Markov operators. Zbl 1073.37091
Ding, Jiu; Zhou, Aihui
2002
A two-grid discretization scheme for eigenvalue problems. Zbl 0959.65119
Xu, Jinchao; Zhou, Aihui
2001
Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems. Zbl 0990.65128
Xu, Jinchao; Zhou, Aihui
2001
Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes. Zbl 0986.65098
Yan, Ningning; Zhou, Aihui
2001
A sparse finite element method with high accuracy. I. Zbl 0989.65134
Lin, Qun; Yan, Ningning; Zhou, Aihui
2001
An analysis of some high accuracy finite element methods for hyperbolic problems. Zbl 1004.65100
Zhou, Aihui
2001
Constructive approximations of Markov operators. Zbl 0991.37004
Ding, Jiu; Zhou, Aihui
2001
Finite volume methods for eigenvalue problems. Zbl 0983.65124
Liang, Shengde; Ma, Xiuling; Zhou, Aihui
2001
On estimating absolutely continuous invariant measures. Zbl 1031.37004
Ding, Jiu; Zhou, Aihui
2001
Local and parallel finite element algorithms based on two-grid discretizations. Zbl 0948.65122
Xu, Jinchao; Zhou, Aihui
2000
Absolutely continuous invariant measures for piecewise $$C^2$$ and expanding mappings in higher dimensions. Zbl 1009.37012
Ding, Jiu; Zhou, Aihui
2000
Error analysis of the combination technique. Zbl 0942.65122
Pflaum, C.; Zhou, A.
1999
A box scheme for coupled systems resulting from microsensor thermistor problems. Zbl 0979.78023
Allegretto, Walter; Lin, Yanping; Zhou, Aihui
1999
Long-time stability of finite element approximations for parabolic equations with memory. Zbl 0931.65136
Allegretto, Walter; Lin, Yanping; Zhou, Aihui
1999
Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem. Zbl 0917.76042
Zhou, Aihui
1999
A finite element method for the Frobenius-Perron operator equation. Zbl 0977.65104
Ding, Jiu; Zhou, Aihui
1999
The projection method for a class of Frobenius-Perron operators. Zbl 0943.47042
Ding, J.; Zhou, A.
1999
Multi-parameter extrapolation methods for boundary integral equations. Zbl 0922.65075
Rüde, Ulrich; Zhou, Aihui
1998
A multi-parameter splitting extrapolation and a parallel algorithm for elliptic eigenvalue problem. Zbl 0905.65106
Liao, Xiaohai; Zhou, Aihui
1998
Error analysis on bi-parameter finite elements. Zbl 0945.65122
Zhou, Aihui; Liem, Chinbo; Shih, Tsimin; Lü, Lao
1998
Invariant measures and their computation. Zbl 1054.37500
Ding, Jiu; Zhou, Aihui
1998
A multi-parameter splitting extrapolation and a parallel algorithm. Zbl 0895.65058
Zhou, Aihui; Liem, Chin-bo; Shih, Tsi-min; Lü, Tao
1997
Multi-parameter error resolution for the collocation method of Volterra integral equations. Zbl 0910.65110
Zhou, Aihui
1997
Finite approximations of Frobenius-Perron operators. A solution of Ulam’s conjecture to multi-dimensional transformations. Zbl 0890.58035
Ding, Jiu; Zhou, Aihui
1996
Global superconvergence approximations of the mixed finite element method for the Stokes problem and the linear elasticity equation. Zbl 0858.73076
Zhou, Aihui
1996
Piecewise linear Markov approximations of Frobenius-Perron operators associated with multi-dimensional transformations. Zbl 0907.47025
Ding, Jiu; Zhou, Ai Hui
1995
Parallel computation and domain decomposition for a class of hyperbolic problems. Zbl 0842.65070
Lin, Qun; Yan, Ningning; Zhou, Aihui
1995
The full approximation accuracy for the stream function-vorticity- pressure method. Zbl 0823.65110
Zhou, Aihui; Li, Jichun
1994
The projection method for computing multidimensional absolutely continuous invariant measures. Zbl 0972.28501
Ding, Jiu; Zhou, Aihui
1994
Optimal and superconvergence estimates of the finite element method for a scalar hyperbolic equation. Zbl 0805.65099
Zhou, Aihui; Lin, Qun
1994
Notes on superconvergence and its related topics. Zbl 0790.65095
Lin, Qun; Zhou, Aihui
1993
Convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. Zbl 0787.65071
Lin, Qun; Zhou, Aihui
1993
Defect correction for finite element gradient. Zbl 0767.65001
Lin, Qun; Zhou, Aihui
1992
Extrapolation for collocation method of the first kind Volterra integral equations. Zbl 0755.65138
Zhou, Aihui
1991
...and 1 more Documents
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#### Cited by 934 Authors

 55 Shi, Dongyang 43 Ding, Jiu 42 Zhou, Aihui 39 Yang, Yidu 31 Xie, Hehu 27 Shang, Yueqiang 25 Bi, Hai 22 Huang, Yunqing 19 He, Yinnian 16 Chen, Yanping 16 Rhee, Noah H. 16 Zhang, Zhimin 15 Lin, Qun 13 Han, Jiayu 13 Li, Jian 12 Du, Guangzhi 12 Hu, Jun 12 Yan, Ningning 10 Chen, Huajie 10 Guan, Hongbo 10 Hou, Yanren 10 Huang, Qiumei 10 Jia, Shanghui 10 Li, Yonghai 10 Zhang, Yu 9 Demlow, Alan 9 Li, Zi-Cai 9 Xu, Yuesheng 9 Zuo, Liyun 8 Bi, Chunjia 8 Carstensen, Carsten 8 Jin, Congming 8 Li, Jichun 8 Zhang, Tie 7 Feng, Xinlong 7 Gong, Wei 7 Huang, Jin 7 Li, Hao 7 Liu, Huipo 7 Madden, Niall 7 Shi, Zhongci 7 Shu, Shi 7 Wang, Cheng 7 Xu, Jinchao 7 Zhang, Shuhua 7 Zhao, Yanmin 6 Bollt, Erik M. 6 Chien, Cheng-Sheng 6 Dai, Xiaoying 6 Gedicke, Joscha 6 Hu, Guanghui 6 Huang, Hung-Tsai 6 Sun, Jiguang 6 Yang, Min 5 Bao, Gang 5 Chen, Chuanjun 5 Chen, Hongtao 5 Chen, Zhangxin 5 Froyland, Gary 5 Giani, Stefano 5 Guo, Hailong 5 He, Xiaoming 5 Ma, Hongkun 5 Mao, Shipeng 5 Międlar, Agnieszka 5 Ovall, Jeffrey S. 5 Si, Zhiyong 5 Tang, Qili 5 Wang, Fenling 5 Wen, Zaiwen 5 Zhang, Shuo 5 Zheng, Haibiao 4 Cancès, Eric 4 Chen, Luoping 4 Grubišić, Luka 4 Huang, Qianglian 4 Jeng, B.-W. 4 Lin, Yanping 4 Lu, Tao 4 Luo, Fusheng 4 Mu, Lin 4 Perotto, Simona 4 Peterseim, Daniel 4 Russell, Stephen J. 4 Shen, Quan 4 Stynes, Martin 4 Wang, Junjun 4 Weng, Zhifeng 4 Xie, ManTing 4 Xu, Chao 4 Yang, Huaijun 4 Yang, Ying 4 Yuan, Ya-xiang 4 Yue, Meiling 4 Zhao, Ren 4 Zhao, Xin 4 Zhong, Liuqiang 4 Zou, Qingsong 3 Boffi, Daniele 3 Cao, Yong ...and 834 more Authors
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#### Cited in 140 Serials

 52 Applied Mathematics and Computation 48 Journal of Scientific Computing 44 Journal of Computational and Applied Mathematics 43 Computers & Mathematics with Applications 37 Advances in Computational Mathematics 31 Mathematics of Computation 30 Applied Numerical Mathematics 27 Journal of Computational Physics 26 Numerische Mathematik 21 Computer Methods in Applied Mechanics and Engineering 21 Science China. Mathematics 19 Numerical Methods for Partial Differential Equations 19 Numerical Algorithms 17 Advances in Applied Mathematics and Mechanics 15 Journal of Mathematical Analysis and Applications 14 SIAM Journal on Scientific Computing 13 Applied Mathematics Letters 11 SIAM Journal on Numerical Analysis 10 Mathematical Methods in the Applied Sciences 10 Applications of Mathematics 10 International Journal of Computer Mathematics 9 BIT 9 Applied Mathematics and Mechanics. (English Edition) 9 Acta Mathematicae Applicatae Sinica. English Series 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Mathematical Problems in Engineering 8 Journal of Systems Science and Complexity 8 Communications in Computational Physics 7 Physica D 6 Linear Algebra and its Applications 6 Abstract and Applied Analysis 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Science in China. Series A 5 Engineering Analysis with Boundary Elements 5 Multiscale Modeling & Simulation 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Chaos, Solitons and Fractals 4 Calcolo 4 SIAM Journal on Matrix Analysis and Applications 4 Computational and Applied Mathematics 4 Computational Methods in Applied Mathematics 4 East Asian Journal on Applied Mathematics 4 Nonlinear Analysis. Theory, Methods & Applications 3 Computer Physics Communications 3 Inverse Problems 3 Journal of Statistical Physics 3 Linear and Multilinear Algebra 3 Computing 3 International Journal for Numerical Methods in Engineering 3 Mathematics and Computers in Simulation 3 Ergodic Theory and Dynamical Systems 3 Journal of Integral Equations and Applications 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Applied Mathematical Modelling 3 Numerical Linear Algebra with Applications 3 Chaos 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Numerical Mathematics 3 SIAM Journal on Applied Dynamical Systems 3 Inverse Problems and Imaging 2 Applicable Analysis 2 Computers and Fluids 2 Numerical Functional Analysis and Optimization 2 Journal of Complexity 2 Journal of Mathematical Chemistry 2 Differential Equations and Dynamical Systems 2 Acta Mathematica Sinica. English Series 2 Engineering Computations 2 Journal of Applied Mathematics and Computing 2 International Journal of Computational Methods 2 International Journal of Numerical Analysis and Modeling 2 Journal of Computational Dynamics 2 Research in the Mathematical Sciences 2 Open Mathematics 2 AMM. Applied Mathematics and Mechanics. (English Edition) 2 Korean Journal of Mathematics 2 Electronic Research Archive 1 Discrete Applied Mathematics 1 International Journal of Theoretical Physics 1 Israel Journal of Mathematics 1 Journal of Mathematical Physics 1 Advances in Mathematics 1 Automatica 1 Functiones et Approximatio. Commentarii Mathematici 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Stochastic Analysis and Applications 1 Bulletin of the Iranian Mathematical Society 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Probability Theory and Related Fields 1 Computational Mechanics 1 Queueing Systems 1 Japan Journal of Industrial and Applied Mathematics 1 Communications in Statistics. Theory and Methods 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Optimization 1 Computational Optimization and Applications 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Monte Carlo Methods and Applications ...and 40 more Serials
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#### Cited in 46 Fields

 662 Numerical analysis (65-XX) 338 Partial differential equations (35-XX) 129 Fluid mechanics (76-XX) 52 Dynamical systems and ergodic theory (37-XX) 35 Linear and multilinear algebra; matrix theory (15-XX) 34 Mechanics of deformable solids (74-XX) 28 Optics, electromagnetic theory (78-XX) 27 Integral equations (45-XX) 27 Quantum theory (81-XX) 24 Operator theory (47-XX) 23 Calculus of variations and optimal control; optimization (49-XX) 22 Statistical mechanics, structure of matter (82-XX) 16 Operations research, mathematical programming (90-XX) 15 Probability theory and stochastic processes (60-XX) 12 Approximations and expansions (41-XX) 12 Statistics (62-XX) 8 Combinatorics (05-XX) 8 Computer science (68-XX) 8 Biology and other natural sciences (92-XX) 7 Ordinary differential equations (34-XX) 6 Systems theory; control (93-XX) 5 Measure and integration (28-XX) 5 Potential theory (31-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Real functions (26-XX) 3 Functional analysis (46-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Commutative algebra (13-XX) 2 Associative rings and algebras (16-XX) 2 Difference and functional equations (39-XX) 2 Differential geometry (53-XX) 2 Mechanics of particles and systems (70-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)