## Cai, Zhiqiang

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 Author ID: cai.zhiqiang Published as: Cai, Zhiqiang; Cai, Z.; Cai, Zhi-qiang; Chai, Zhiqiang more...less
 Documents Indexed: 103 Publications since 1986 1 Contribution as Editor Co-Authors: 77 Co-Authors with 89 Joint Publications 2,280 Co-Co-Authors
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### Co-Authors

 6 single-authored 16 Zhang, Shun 14 McCormick, Steve Fahrney 9 Manteuffel, Thomas A. 7 Ye, Xiu 6 Kim, Seokchan 6 Liu, Min 5 Chen, Jingshuang 5 Douglas, Jim jun. 5 He, Cuiyu 5 Ku, Jaeun 4 Si, Shubin 4 Starke, Gerhard 3 Cai, Difeng 3 Dui, Hongyan 3 Sun, Shudong 3 Wang, Yanqiu 2 Cao, Shuhao 2 Dawson, Darren M. 2 de Queiroz, Marcio S. 2 Du, Shaohong 2 Falgout, Rob 2 Lee, Chang-Ock 2 Mandel, Jan 2 Park, Moongyu 2 Russell, Thomas F. 2 Shin, Byeong Chun 2 Wang, Chunbo 2 Wang, Nengchao 2 Westphal, Chad R. 2 Zhang, Yingfeng 1 Aikawa, K. 1 Attia, Frank S. 1 Bank, Randolph E. 1 Baranov, M. A. 1 Bertrand, Fleurianne 1 Bochev, Pavel B. 1 Carey, Varis 1 Chen, Binghe 1 Chomaz, L. 1 Du, Ding-Zhu 1 Duan, Dongli 1 E, Weinan 1 Ferlaino, F. 1 Goldstein, Charles I. 1 Guo, Ben-Yu 1 Hao, Zhaopeng 1 Hou, Thomas Yizhao 1 Hou, Yanren 1 Jones, Jim E. 1 Kang, Lishan 1 Kim, Sangdong 1 Kong, Sooryoun 1 Kong, Sooryun 1 Korsawe, Johannes 1 Lai, Chen-Yao G. 1 Lazarov, Raytcho D. 1 Lee, Barry 1 Lee, Hyung-Chun 1 Lin, Guang 1 Liu, Xinyu 1 Mark, M. J. 1 Meng, Xueyu 1 Parashkevov, Rossen R. 1 Park, Eun-Jae 1 Park, Eunyoung 1 Parter, Seymour V. 1 Pasciak, Joseph E. 1 Petter, D. 1 Pyo, Jae-Hong 1 Qi, Huan 1 Ruge, J. 1 Santos, Juan Enrique 1 Saygin, Can 1 Sheen, Dongwoo 1 Song, Lina 1 Song, Xiaoyu 1 Thai, My T. 1 Vassilevski, Panayot Spirov 1 Verfürth, Rüdiger 1 Wang, Junbo 1 Wang, Ning 1 Wilson, John David 1 Woo, Gyungsoo 1 Wu, Xiaohui 1 Xia, Jun 1 Zhang, Huilong 1 Zhang, Shuai 1 Zhao, Xibin 1 Zoller, Peter
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### Serials

 30 SIAM Journal on Numerical Analysis 7 Computer Methods in Applied Mechanics and Engineering 6 Numerical Methods for Partial Differential Equations 5 SIAM Journal on Scientific Computing 4 Computers & Mathematics with Applications 4 Mathematics of Computation 3 Journal of Computational Physics 3 Applied Mathematics and Computation 3 Journal of Scientific Computing 3 Communications in Statistics. Theory and Methods 3 Numerical Linear Algebra with Applications 2 Calcolo 2 IEEE Transactions on Automatic Control 2 Numerische Mathematik 2 Applied Numerical Mathematics 1 Acta Mechanica 1 Classical and Quantum Gravity 1 International Journal for Numerical Methods in Fluids 1 Hokkaido Mathematical Journal 1 Journal of Computational and Applied Mathematics 1 Numerical Mathematics 1 Mathematica Numerica Sinica 1 Journal of Computational Mathematics 1 Communications in Applied Numerical Methods 1 International Journal of High Speed Computing 1 Journal of Non-Newtonian Fluid Mechanics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Mathematical Problems in Engineering 1 Optimization Methods & Software 1 Journal of Ningxia University. Natural Science Edition 1 Computational Geosciences 1 Computational Methods in Applied Mathematics 1 Communications in Mathematical Sciences 1 Journal of Computational Mathematics and Optimization 1 Oberwolfach Reports 1 Science
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### Fields

 76 Numerical analysis (65-XX) 47 Partial differential equations (35-XX) 25 Fluid mechanics (76-XX) 17 Mechanics of deformable solids (74-XX) 4 Probability theory and stochastic processes (60-XX) 4 Statistics (62-XX) 4 Computer science (68-XX) 4 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

86 Publications have been cited 1,895 times in 1,159 Documents Cited by Year
On the finite volume element method. Zbl 0731.65093
Cai, Zhiqiang
1991
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Zbl 0922.65071
Hou, Thomas Y.; Wu, Xiao-Hui; Cai, Zhiqiang
1999
First-order system least squares for second-order partial differential equations. I. Zbl 0813.65119
Cai, Z.; Lazarov, R.; Manteuffel, T. A.; McCormick, S. F.
1994
The finite volume element method for diffusion equations on general triangulations. Zbl 0729.65086
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
1991
On the accuracy of the finite volume element method for diffusion equations on composite grids. Zbl 0707.65073
Cai, Zhiqiang; McCormick, Steve
1990
First-order system least squares for second-order partial differential equations: Part II. Zbl 0912.65089
Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.
1997
First-order system least squares for the Stokes equations, with application to linear elasticity. Zbl 0901.76052
Cai, Z.; Manteuffel, T. A.; McCormick, S. F.
1997
Discontinuous Galerkin finite element methods for interface problems: a priori and a posteriori error estimations. Zbl 1232.65142
Cai, Zhiqiang; Ye, Xiu; Zhang, Shun
2011
A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations. Zbl 0947.76047
Cai, Zhiqiang; Douglas, Jim jun.; Ye, Xiu
1999
Control-volume mixed finite element methods. Zbl 0941.76050
Cai, Z.; Jones, J. E.; McCormick, S. F.; Russell, T. F.
1997
Analysis of velocity-flux first-order system least-squares principles for the Navier-Stokes equations. I. Zbl 0910.76032
Bochev, P.; Cai, Z.; Manteuffel, T. A.; McCormick, S. F.
1998
Least-squares methods for incompressible Newtonian fluid flow: linear stationary problems. Zbl 1159.76347
Cai, Zhiqiang; Lee, Barry; Wang, Ping
2004
Least-squares methods for linear elasticity. Zbl 1159.74419
Cai, Zhiqiang; Starke, Gerhard
2004
Recovery-based error estimator for interface problems: Conforming linear elements. Zbl 1204.65129
Cai, Zhiqiang; Zhang, Shun
2009
A finite element method using singular functions for the Poisson equation: Corner singularities. Zbl 0992.65122
Cai, Zhiqiang; Kim, Seokchan
2001
Development and analysis of higher order finite volume methods over rectangles for elliptic equations. Zbl 1020.65087
Cai, Zhiqiang; Douglas, Jim jun.; Park, Moongyu
2003
Mixed finite element methods for incompressible flow: stationary Stokes equations. Zbl 1267.76059
Cai, Zhiqiang; Tong, Charles; Vassilevski, Panayot S.; Wang, Chunbo
2010
First-order system least squares for the stress-displacement formulation: Linear elasticity. Zbl 1063.74099
Cai, Zhiqiang; Starke, Gerhard
2003
Recovery-based error estimators for interface problems: mixed and nonconforming finite elements. Zbl 1210.65185
Cai, Zhiqiang; Zhang, Shun
2010
Robust adaptive asymptotic tracking of nonlinear systems with additive disturbance. Zbl 1366.93565
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
2006
First-order system least squares for velocity-vorticity-pressure form of the Stokes equations, with application to linear elasticity. Zbl 0856.76010
Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.
1995
Nonconforming quadrilateral finite elements: a correction. Zbl 1012.65124
Cai, Z.; Douglas, J. jun.; Santos, J. E.; Sheen, D.; Ye, X.
2000
A sufficiently smooth projection operator. Zbl 1366.93283
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
2006
Discontinuous finite element methods for interface problems: robust a priori and a posteriori error estimates. Zbl 1359.65248
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2017
A multigrid method for the pseudostress formulation of Stokes problems. Zbl 1182.76896
Cai, Zhiqiang; Wang, Yanqiu
2007
Robust equilibrated residual error estimator for diffusion problems: conforming elements. Zbl 1253.65175
Cai, Zhiqiang; Zhang, Shun
2012
First-order system least squares (FOSLS) for planar linear elasticity: Pure traction problem. Zbl 0968.74061
Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.; Parter, Seymour V.
1998
An adaptive mixed least-squares finite element method for viscoelastic fluids of Oldroyd type. Zbl 1274.76246
Cai, Z.; Westphal, C. R.
2009
Mixed finite element methods for incompressible flow: stationary Navier-Stokes equations. Zbl 1410.76160
Cai, Zhiqiang; Wang, Chunbo; Zhang, Shun
2010
Flux recovery and a posteriori error estimators: conforming elements for scalar elliptic equations. Zbl 1230.65117
Cai, Zhiqiang; Zhang, Shun
2010
First-order system $$\mathcal L\mathcal L^*$$ (FOSLL*): Scalar elliptic partial differential equations. Zbl 1008.65085
Cai, Z.; Manteuffel, T. A.; McCormick, S. F.; Ruge, J.
2001
An adaptive least squares mixed finite element method for the stress-displacement formulation of linear elasticity. Zbl 1061.74050
Cai, Zhiqiang; Korsawe, Johannes; Starke, Gerhard
2005
Multigrid methods for nearly singular linear equations and eigenvalue problems. Zbl 0873.65030
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
1997
Solution methods for the Poisson equation with corner singularities: Numerical results. Zbl 0991.65117
Cai, Zhiqiang; Kim, Seokchan; Shin, Byeong-Chun
2001
The $$L^2$$ norm error estimates for the div least-squares method. Zbl 1138.76053
Cai, Zhiqiang; Ku, Jaeun
2006
A mixed nonconforming finite element for linear elasticity. Zbl 1076.74053
Cai, Zhiqiang; Ye, Xiu
2005
Multilevel iteration for mixed finite element systems with penalty. Zbl 0809.65114
Cai, Zhiqiang; Goldstein, Charles I.; Pasciak, Joseph E.
1993
Finite element method for two-sided fractional differential equations with variable coefficients: Galerkin approach. Zbl 1416.65268
Hao, Zhaopeng; Park, Moongyu; Lin, Guang; Cai, Zhiqiang
2019
Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. Zbl 1307.76050
Cai, Zhiqiang; Zhang, Shun
2012
A weighted $$H$$(div) least-squares method for second-order elliptic problems. Zbl 1168.65069
Cai, Z.; Westphal, C. R.
2008
A finite element method using singular functions for Poisson equations: Mixed boundary conditions. Zbl 1124.65108
Cai, Zhiqiang; Kim, Seokchan; Kim, Sangdong; Kong, Sooryun
2006
Recovery-based error estimator for stabilized finite element methods for the Stokes equation. Zbl 1296.76087
Song, Lina; Hou, Yanren; Cai, Zhiqiang
2014
Pseudostress-velocity formulation for incompressible Navier-Stokes equations. Zbl 1352.76043
Cai, Zhiqiang; Wang, Yanqiu
2010
A recovery-based a posteriori error estimator for $$H$$(curl) interface problems. Zbl 1425.65153
Cai, Zhiqiang; Cao, Shuhao
2015
First-order system least squares for linear elasticity: Numerical results. Zbl 0988.74061
Cai, Z.; Lee, C.-O.; Manteuffel, T. A.; McCormick, S. F.
2000
Optimal error estimate for the div least-squares method with data $$f\in L^2$$ and application to nonlinear problems. Zbl 1275.65079
Cai, Zhiqiang; Ku, Jaeun
2010
Residual-based a posteriori error estimate for interface problems: nonconforming linear elements. Zbl 1355.65145
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2017
First-order system least squares for the Stokes and linear elasticity equations: Further results. Zbl 0968.76035
Cai, Z.; Lee, C.-O.; Manteuffel, T. A.; McCormick, S. F.
2000
An error estimate for two-dimensional Stokes driven cavity flow. Zbl 1198.65217
Cai, Zhiqiang; Wang, Yanqiu
2009
Least-squares finite element approximations for the Reissner-Mindlin plate. Zbl 0982.74062
Chai, Zhiqiang; Ye, Xiu; Zhang, Huilong
1999
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs. Zbl 07506625
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min; Liu, Xinyu
2020
Domain decomposition for a mixed finite element method in three dimensions. Zbl 1057.65095
Cai, Z.; Parashkevov, R. R.; Russell, T. F.; Wilson, J. D.; Ye, X.
2003
A least-squares finite element approximation for the compressible Stokes equations. Zbl 0965.76039
Cai, Zhiqiang; Ye, Xiu
2000
Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Zbl 1447.65130
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
2020
Improved ZZ a posteriori error estimators for diffusion problems: conforming linear elements. Zbl 1439.65153
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2017
A dual finite element method for a singularly perturbed reaction-diffusion problem. Zbl 1440.65188
Cai, Zhiqiang; Ku, JaEun
2020
Div first-order system LL* (FOSLL*) for second-order elliptic partial differential equations. Zbl 1312.65005
Cai, Zhiqiang; Falgout, Rob; Zhang, Shun
2015
Goal-oriented local a posteriori error estimators for $$H(\text{div})$$ least-squares finite element methods. Zbl 1298.65147
Cai, Zhiqiang; Ku, JaEun
2011
Robust a posteriori error estimation for finite element approximation to $$\boldsymbol{H}(\mathbf{curl})$$ problem. Zbl 1439.78019
Cai, Zhiqiang; Cao, Shuhao; Falgout, Rob
2016
Robust equilibrated error estimator for diffusion problems: mixed finite elements in two dimensions. Zbl 1437.65177
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
2020
A finite element method using singular functions: interface problems. Zbl 1140.65084
Kim, Seokchan; Cai, Zhiqiang; Pyo, Jae-Hong; Kong, Sooryoun
2007
Robust residual- and recovery-based a posteriori error estimators for interface problems with flux jumps. Zbl 1245.65148
Cai, Zhiqiang; Zhang, Shun
2012
First-order system least squares for the Signorini contact problem in linear elasticity. Zbl 1410.74058
Attia, Frank S.; Cai, Zhiqiang; Starke, Gerhard
2009
Least squares for the perturbed Stokes equations and the Reissner–Mindlin plate. Zbl 1003.76047
Cai, Zhiqiang
2000
The discrete first-order system least squares: The second-order elliptic boundary value problem. Zbl 1017.65092
Cai, Zhiqiang; Shin, Byeong Chun
2002
Extended Bose-Hubbard models with ultracold magnetic atoms. Zbl 1355.81173
Baier, S.; Mark, M. J.; Petter, D.; Aikawa, K.; Chomaz, L.; Cai, Z.; Baranov, M.; Zoller, P.; Ferlaino, F.
2016
Least-squares method for the Oseen equation. Zbl 1407.76026
Cai, Zhiqiang; Chen, Binghe
2016
Analysis of epidemic vaccination strategies on heterogeneous networks: based on SEIRV model and evolutionary game. Zbl 07423617
Meng, Xueyu; Cai, Zhiqiang; Si, Shubin; Duan, Dongli
2021
Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements. Zbl 1478.65116
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2021
A hybrid a posteriori error estimator for conforming finite element approximations. Zbl 1440.65187
Cai, Difeng; Cai, Zhiqiang
2018
Stabilized finite element methods with fast iterative solution algorithms for the Stokes problem. Zbl 0943.76048
Cai, Zhiqiang; Douglas, Jim jun.
1998
Norm estimates of product operators with application to domain decomposition. Zbl 0766.65100
Cai, Zhiqiang
1993
Uniform asymptotic analysis for transient waves in a pre-stressed compressible hyperelastic rod. Zbl 0982.74038
Dai, H.-H.; Cai, Z.
2000
Convergence estimates of multilevel additive and multiplicative algorithms for non-symmetric and indefinite problems. Zbl 0852.65112
Cai, Zhiqiang; Lai, Chen-Yao G.
1996
An analytic basis for multigrid methods for stabilized finite element methods for the Stokes problem. Zbl 0911.65124
Cai, Z.; Douglas, J. jun.
1997
A finite element method using singular functions for the Poisson equation: crack singularities. Zbl 1071.65152
Cai, Zhiqiang; Kim, Seokchan; Woo, Gyungsoo
2002
Computational complexity of the Schwarz alternating procedure. Zbl 0726.65029
Cai, Zhiqiang; McCormick, Steve
1989
Error estimate of a finite element method using stress intensity factor. Zbl 1442.65348
Cai, Zhiqiang; Kim, Seokchan; Lee, Hyung-Chun
2018
Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global $$L_2$$ norm. Zbl 1443.65315
Cai, Zhiqiang; Carey, Varis; Ku, JaEun; Park, Eun-Jae
2015
Error estimates for a Schwarz alternating procedure on L-shaped regions. Zbl 0655.65113
Cai, Zhiqiang; Guo, Benju
1988
Least-squares methods for elasticity and Stokes equations with weakly imposed symmetry. Zbl 1420.65115
Bertrand, Fleurianne; Cai, Zhiqiang; Park, Eun Young
2019
Analytic spectra of CMB anisotropies and polarization generated by scalar perturbations in synchronous gauge. Zbl 1242.85011
Cai, Z.; Zhang, Y.
2012
Joint integrated importance measure for multi-state transition systems. Zbl 1284.90018
Si, Shubin; Dui, Hongyan; Cai, Zhiqiang; Sun, Shudong; Zhang, Yingfeng
2012
Improved ZZ a posteriori error estimators for diffusion problems: discontinuous elements. Zbl 1460.65143
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2021
Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law. Zbl 1484.65174
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
2022
Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation. Zbl 07515414
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
2021
Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law. Zbl 1484.65174
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
2022
Analysis of epidemic vaccination strategies on heterogeneous networks: based on SEIRV model and evolutionary game. Zbl 07423617
Meng, Xueyu; Cai, Zhiqiang; Si, Shubin; Duan, Dongli
2021
Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements. Zbl 1478.65116
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2021
Improved ZZ a posteriori error estimators for diffusion problems: discontinuous elements. Zbl 1460.65143
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2021
Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation. Zbl 07515414
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
2021
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs. Zbl 07506625
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min; Liu, Xinyu
2020
Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Zbl 1447.65130
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
2020
A dual finite element method for a singularly perturbed reaction-diffusion problem. Zbl 1440.65188
Cai, Zhiqiang; Ku, JaEun
2020
Robust equilibrated error estimator for diffusion problems: mixed finite elements in two dimensions. Zbl 1437.65177
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
2020
Finite element method for two-sided fractional differential equations with variable coefficients: Galerkin approach. Zbl 1416.65268
Hao, Zhaopeng; Park, Moongyu; Lin, Guang; Cai, Zhiqiang
2019
Least-squares methods for elasticity and Stokes equations with weakly imposed symmetry. Zbl 1420.65115
Bertrand, Fleurianne; Cai, Zhiqiang; Park, Eun Young
2019
A hybrid a posteriori error estimator for conforming finite element approximations. Zbl 1440.65187
Cai, Difeng; Cai, Zhiqiang
2018
Error estimate of a finite element method using stress intensity factor. Zbl 1442.65348
Cai, Zhiqiang; Kim, Seokchan; Lee, Hyung-Chun
2018
Discontinuous finite element methods for interface problems: robust a priori and a posteriori error estimates. Zbl 1359.65248
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2017
Residual-based a posteriori error estimate for interface problems: nonconforming linear elements. Zbl 1355.65145
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2017
Improved ZZ a posteriori error estimators for diffusion problems: conforming linear elements. Zbl 1439.65153
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
2017
Robust a posteriori error estimation for finite element approximation to $$\boldsymbol{H}(\mathbf{curl})$$ problem. Zbl 1439.78019
Cai, Zhiqiang; Cao, Shuhao; Falgout, Rob
2016
Extended Bose-Hubbard models with ultracold magnetic atoms. Zbl 1355.81173
Baier, S.; Mark, M. J.; Petter, D.; Aikawa, K.; Chomaz, L.; Cai, Z.; Baranov, M.; Zoller, P.; Ferlaino, F.
2016
Least-squares method for the Oseen equation. Zbl 1407.76026
Cai, Zhiqiang; Chen, Binghe
2016
A recovery-based a posteriori error estimator for $$H$$(curl) interface problems. Zbl 1425.65153
Cai, Zhiqiang; Cao, Shuhao
2015
Div first-order system LL* (FOSLL*) for second-order elliptic partial differential equations. Zbl 1312.65005
Cai, Zhiqiang; Falgout, Rob; Zhang, Shun
2015
Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global $$L_2$$ norm. Zbl 1443.65315
Cai, Zhiqiang; Carey, Varis; Ku, JaEun; Park, Eun-Jae
2015
Recovery-based error estimator for stabilized finite element methods for the Stokes equation. Zbl 1296.76087
Song, Lina; Hou, Yanren; Cai, Zhiqiang
2014
Robust equilibrated residual error estimator for diffusion problems: conforming elements. Zbl 1253.65175
Cai, Zhiqiang; Zhang, Shun
2012
Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. Zbl 1307.76050
Cai, Zhiqiang; Zhang, Shun
2012
Robust residual- and recovery-based a posteriori error estimators for interface problems with flux jumps. Zbl 1245.65148
Cai, Zhiqiang; Zhang, Shun
2012
Analytic spectra of CMB anisotropies and polarization generated by scalar perturbations in synchronous gauge. Zbl 1242.85011
Cai, Z.; Zhang, Y.
2012
Joint integrated importance measure for multi-state transition systems. Zbl 1284.90018
Si, Shubin; Dui, Hongyan; Cai, Zhiqiang; Sun, Shudong; Zhang, Yingfeng
2012
Discontinuous Galerkin finite element methods for interface problems: a priori and a posteriori error estimations. Zbl 1232.65142
Cai, Zhiqiang; Ye, Xiu; Zhang, Shun
2011
Goal-oriented local a posteriori error estimators for $$H(\text{div})$$ least-squares finite element methods. Zbl 1298.65147
Cai, Zhiqiang; Ku, JaEun
2011
Mixed finite element methods for incompressible flow: stationary Stokes equations. Zbl 1267.76059
Cai, Zhiqiang; Tong, Charles; Vassilevski, Panayot S.; Wang, Chunbo
2010
Recovery-based error estimators for interface problems: mixed and nonconforming finite elements. Zbl 1210.65185
Cai, Zhiqiang; Zhang, Shun
2010
Mixed finite element methods for incompressible flow: stationary Navier-Stokes equations. Zbl 1410.76160
Cai, Zhiqiang; Wang, Chunbo; Zhang, Shun
2010
Flux recovery and a posteriori error estimators: conforming elements for scalar elliptic equations. Zbl 1230.65117
Cai, Zhiqiang; Zhang, Shun
2010
Pseudostress-velocity formulation for incompressible Navier-Stokes equations. Zbl 1352.76043
Cai, Zhiqiang; Wang, Yanqiu
2010
Optimal error estimate for the div least-squares method with data $$f\in L^2$$ and application to nonlinear problems. Zbl 1275.65079
Cai, Zhiqiang; Ku, Jaeun
2010
Recovery-based error estimator for interface problems: Conforming linear elements. Zbl 1204.65129
Cai, Zhiqiang; Zhang, Shun
2009
An adaptive mixed least-squares finite element method for viscoelastic fluids of Oldroyd type. Zbl 1274.76246
Cai, Z.; Westphal, C. R.
2009
An error estimate for two-dimensional Stokes driven cavity flow. Zbl 1198.65217
Cai, Zhiqiang; Wang, Yanqiu
2009
First-order system least squares for the Signorini contact problem in linear elasticity. Zbl 1410.74058
Attia, Frank S.; Cai, Zhiqiang; Starke, Gerhard
2009
A weighted $$H$$(div) least-squares method for second-order elliptic problems. Zbl 1168.65069
Cai, Z.; Westphal, C. R.
2008
A multigrid method for the pseudostress formulation of Stokes problems. Zbl 1182.76896
Cai, Zhiqiang; Wang, Yanqiu
2007
A finite element method using singular functions: interface problems. Zbl 1140.65084
Kim, Seokchan; Cai, Zhiqiang; Pyo, Jae-Hong; Kong, Sooryoun
2007
Robust adaptive asymptotic tracking of nonlinear systems with additive disturbance. Zbl 1366.93565
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
2006
A sufficiently smooth projection operator. Zbl 1366.93283
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
2006
The $$L^2$$ norm error estimates for the div least-squares method. Zbl 1138.76053
Cai, Zhiqiang; Ku, Jaeun
2006
A finite element method using singular functions for Poisson equations: Mixed boundary conditions. Zbl 1124.65108
Cai, Zhiqiang; Kim, Seokchan; Kim, Sangdong; Kong, Sooryun
2006
An adaptive least squares mixed finite element method for the stress-displacement formulation of linear elasticity. Zbl 1061.74050
Cai, Zhiqiang; Korsawe, Johannes; Starke, Gerhard
2005
A mixed nonconforming finite element for linear elasticity. Zbl 1076.74053
Cai, Zhiqiang; Ye, Xiu
2005
Least-squares methods for incompressible Newtonian fluid flow: linear stationary problems. Zbl 1159.76347
Cai, Zhiqiang; Lee, Barry; Wang, Ping
2004
Least-squares methods for linear elasticity. Zbl 1159.74419
Cai, Zhiqiang; Starke, Gerhard
2004
Development and analysis of higher order finite volume methods over rectangles for elliptic equations. Zbl 1020.65087
Cai, Zhiqiang; Douglas, Jim jun.; Park, Moongyu
2003
First-order system least squares for the stress-displacement formulation: Linear elasticity. Zbl 1063.74099
Cai, Zhiqiang; Starke, Gerhard
2003
Domain decomposition for a mixed finite element method in three dimensions. Zbl 1057.65095
Cai, Z.; Parashkevov, R. R.; Russell, T. F.; Wilson, J. D.; Ye, X.
2003
The discrete first-order system least squares: The second-order elliptic boundary value problem. Zbl 1017.65092
Cai, Zhiqiang; Shin, Byeong Chun
2002
A finite element method using singular functions for the Poisson equation: crack singularities. Zbl 1071.65152
Cai, Zhiqiang; Kim, Seokchan; Woo, Gyungsoo
2002
A finite element method using singular functions for the Poisson equation: Corner singularities. Zbl 0992.65122
Cai, Zhiqiang; Kim, Seokchan
2001
First-order system $$\mathcal L\mathcal L^*$$ (FOSLL*): Scalar elliptic partial differential equations. Zbl 1008.65085
Cai, Z.; Manteuffel, T. A.; McCormick, S. F.; Ruge, J.
2001
Solution methods for the Poisson equation with corner singularities: Numerical results. Zbl 0991.65117
Cai, Zhiqiang; Kim, Seokchan; Shin, Byeong-Chun
2001
Nonconforming quadrilateral finite elements: a correction. Zbl 1012.65124
Cai, Z.; Douglas, J. jun.; Santos, J. E.; Sheen, D.; Ye, X.
2000
First-order system least squares for linear elasticity: Numerical results. Zbl 0988.74061
Cai, Z.; Lee, C.-O.; Manteuffel, T. A.; McCormick, S. F.
2000
First-order system least squares for the Stokes and linear elasticity equations: Further results. Zbl 0968.76035
Cai, Z.; Lee, C.-O.; Manteuffel, T. A.; McCormick, S. F.
2000
A least-squares finite element approximation for the compressible Stokes equations. Zbl 0965.76039
Cai, Zhiqiang; Ye, Xiu
2000
Least squares for the perturbed Stokes equations and the Reissner–Mindlin plate. Zbl 1003.76047
Cai, Zhiqiang
2000
Uniform asymptotic analysis for transient waves in a pre-stressed compressible hyperelastic rod. Zbl 0982.74038
Dai, H.-H.; Cai, Z.
2000
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Zbl 0922.65071
Hou, Thomas Y.; Wu, Xiao-Hui; Cai, Zhiqiang
1999
A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations. Zbl 0947.76047
Cai, Zhiqiang; Douglas, Jim jun.; Ye, Xiu
1999
Least-squares finite element approximations for the Reissner-Mindlin plate. Zbl 0982.74062
Chai, Zhiqiang; Ye, Xiu; Zhang, Huilong
1999
Analysis of velocity-flux first-order system least-squares principles for the Navier-Stokes equations. I. Zbl 0910.76032
Bochev, P.; Cai, Z.; Manteuffel, T. A.; McCormick, S. F.
1998
First-order system least squares (FOSLS) for planar linear elasticity: Pure traction problem. Zbl 0968.74061
Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.; Parter, Seymour V.
1998
Stabilized finite element methods with fast iterative solution algorithms for the Stokes problem. Zbl 0943.76048
Cai, Zhiqiang; Douglas, Jim jun.
1998
First-order system least squares for second-order partial differential equations: Part II. Zbl 0912.65089
Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.
1997
First-order system least squares for the Stokes equations, with application to linear elasticity. Zbl 0901.76052
Cai, Z.; Manteuffel, T. A.; McCormick, S. F.
1997
Control-volume mixed finite element methods. Zbl 0941.76050
Cai, Z.; Jones, J. E.; McCormick, S. F.; Russell, T. F.
1997
Multigrid methods for nearly singular linear equations and eigenvalue problems. Zbl 0873.65030
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
1997
An analytic basis for multigrid methods for stabilized finite element methods for the Stokes problem. Zbl 0911.65124
Cai, Z.; Douglas, J. jun.
1997
Convergence estimates of multilevel additive and multiplicative algorithms for non-symmetric and indefinite problems. Zbl 0852.65112
Cai, Zhiqiang; Lai, Chen-Yao G.
1996
First-order system least squares for velocity-vorticity-pressure form of the Stokes equations, with application to linear elasticity. Zbl 0856.76010
Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.
1995
First-order system least squares for second-order partial differential equations. I. Zbl 0813.65119
Cai, Z.; Lazarov, R.; Manteuffel, T. A.; McCormick, S. F.
1994
Multilevel iteration for mixed finite element systems with penalty. Zbl 0809.65114
Cai, Zhiqiang; Goldstein, Charles I.; Pasciak, Joseph E.
1993
Norm estimates of product operators with application to domain decomposition. Zbl 0766.65100
Cai, Zhiqiang
1993
On the finite volume element method. Zbl 0731.65093
Cai, Zhiqiang
1991
The finite volume element method for diffusion equations on general triangulations. Zbl 0729.65086
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
1991
On the accuracy of the finite volume element method for diffusion equations on composite grids. Zbl 0707.65073
Cai, Zhiqiang; McCormick, Steve
1990
Computational complexity of the Schwarz alternating procedure. Zbl 0726.65029
Cai, Zhiqiang; McCormick, Steve
1989
Error estimates for a Schwarz alternating procedure on L-shaped regions. Zbl 0655.65113
Cai, Zhiqiang; Guo, Benju
1988
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### Cited by 1,361 Authors

 30 Cai, Zhiqiang 21 Zou, Qingsong 19 Yang, Suh-Yuh 18 Zhang, Zhimin 17 Cui, Junzhi 17 Rui, Hongxing 16 Bi, Chunjia 16 Chen, Chuanjun 16 Li, Yonghai 16 Luo, Zhendong 16 Mu, Lin 16 Ye, Xiu 16 Zhang, Shun 15 Yuan, Yirang 14 Chen, Zhangxin 13 Chen, Yanping 13 Li, Jian 12 Gatica, Gabriel N. 12 Manteuffel, Thomas A. 12 Park, Eun-Jae 12 Shi, Dongyang 12 Yang, Min 11 Ku, Jaeun 10 Abdulle, Assyr 10 Feng, Xinlong 10 Guo, Hui 10 He, Wenming 10 Hou, Thomas Yizhao 10 Kim, Sangdong 10 Kim, Seokchan 10 Li, Changfeng 10 Li, Hong 10 Ruiz-Baier, Ricardo 10 Sheen, Dongwoo 10 Starke, Gerhard 10 Wang, Junping 9 Bertrand, Fleurianne 9 He, Cuiyu 9 Huang, Yunqing 9 Lazarov, Raytcho D. 9 Lee, Eunjung 9 Vassilevski, Panayot Spirov 9 Wu, Jiming 9 Xu, Jinchao 9 Zhang, Zhiyue 8 Cao, Liqun 8 Cao, Waixiang 8 Carstensen, Carsten 8 Deng, Weibing 8 Lin, Yanping 8 Liu, Wei 8 McCormick, Steve Fahrney 8 Schröder, Jörg 8 Schwarz, Alexander 8 Valentin, Frédéric 8 Zhang, Tie 7 Chen, Jinru 7 Dehghan Takht Fooladi, Mehdi 7 Guan, Xiaofei 7 Mao, Shipeng 7 Oyarzúa, Ricardo 7 Shin, Byeong Chun 6 Cangiani, Andrea 6 Chen, Shaochun 6 Choi, Hyungjun 6 Dong, Hao 6 Gerritsma, Marc I. 6 Ginting, Victor 6 He, Yinnian 6 Hessari, Peyman 6 Huang, Pengzhan 6 Kumar, Sarvesh 6 Lee, Hsueh-Chen 6 Li, Minghao 6 Luo, Zhongxuan 6 Meng, Zhaoliang 6 Song, Huailing 6 Song, Lina 6 Wang, Hong 6 Wang, Yanqiu 6 Xie, Xiaoping 6 Yang, Danping 6 Yang, Qing 6 Zabaras, Nicholas J. 6 Zhang, Zhiwen 5 Adler, James H. 5 Brenner, Susanne Cecelia 5 Cao, Shuhao 5 Chen, Huangxin 5 Demkowicz, Leszek F. 5 Duan, Huoyuan 5 Fang, Zhichao 5 Fu, Hongfei 5 Hajibeygi, Hadi 5 Heys, Jeffrey J. 5 Hu, Jun 5 Huang, Xuehai 5 Jenny, Patrick 5 Jeon, Youngmok 5 Kwak, Do Young ...and 1,261 more Authors
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### Cited in 135 Serials

 97 Journal of Computational and Applied Mathematics 86 Computer Methods in Applied Mechanics and Engineering 79 Computers & Mathematics with Applications 69 Journal of Computational Physics 60 Applied Mathematics and Computation 59 Journal of Scientific Computing 58 Applied Numerical Mathematics 48 Numerical Methods for Partial Differential Equations 41 Numerische Mathematik 37 SIAM Journal on Numerical Analysis 34 Mathematics of Computation 21 Advances in Computational Mathematics 19 Multiscale Modeling & Simulation 18 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 18 International Journal of Computer Mathematics 18 SIAM Journal on Scientific Computing 17 International Journal for Numerical Methods in Engineering 15 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 Advances in Applied Mathematics and Mechanics 12 Computational Methods in Applied Mathematics 11 Journal of Mathematical Analysis and Applications 11 Mathematical Methods in the Applied Sciences 11 Numerical Linear Algebra with Applications 11 Computational Geosciences 10 Numerical Functional Analysis and Optimization 9 Computing 9 Journal of Numerical Mathematics 8 Numerical Algorithms 8 International Journal of Numerical Analysis and Modeling 8 Science China. Mathematics 7 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 6 International Journal for Numerical Methods in Fluids 6 Calcolo 6 Applications of Mathematics 6 Mathematical Problems in Engineering 6 Computing and Visualization in Science 6 Communications in Computational Physics 5 BIT 5 Mathematics and Computers in Simulation 5 Applied Mathematical Modelling 5 Abstract and Applied Analysis 5 International Journal of Computational Methods 5 East Asian Journal on Applied Mathematics 4 Computational Mechanics 4 Journal of Systems Science and Complexity 4 Journal of Applied Mathematics and Computing 3 International Journal of Modern Physics B 3 Applicable Analysis 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Applied Mathematics and Mechanics. (English Edition) 3 Chinese Annals of Mathematics. Series B 3 Acta Mathematicae Applicatae Sinica. English Series 3 Communications in Numerical Methods in Engineering 3 Computational and Applied Mathematics 3 Foundations of Computational Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 3 Boletim da Sociedade Paranaense de Matemática. Terceira Série 3 Advances in Difference Equations 3 Electronic Research Archive 2 Acta Mechanica 2 Journal of Fluid Mechanics 2 Journal of Computational Mathematics 2 Applied Mathematics Letters 2 Mathematical and Computer Modelling 2 Science in China. Series A 2 Japan Journal of Industrial and Applied Mathematics 2 Journal of Elasticity 2 ETNA. Electronic Transactions on Numerical Analysis 2 International Journal of Computational Fluid Dynamics 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 Honam Mathematical Journal 2 Journal of Inequalities and Applications 2 Journal of Applied Mathematics 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Communications on Pure and Applied Analysis 2 Central European Journal of Mathematics 2 Communications in Applied Mathematics and Computational Science 2 Computational & Mathematical Methods in Medicine 2 Discrete and Continuous Dynamical Systems. Series S 2 East Asian Mathematical Journal 2 Journal of the Korean Society for Industrial and Applied Mathematics 2 Journal of Mathematics 2 AMM. Applied Mathematics and Mechanics. (English Edition) 2 AIMS Mathematics 2 Communications on Applied Mathematics and Computation 1 Computers and Fluids 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Engineering Mathematics 1 Journal of the Franklin Institute 1 Journal of Mathematical Physics 1 Chaos, Solitons and Fractals 1 Siberian Mathematical Journal 1 Optimal Control Applications & Methods 1 Computer Aided Geometric Design 1 COMPEL 1 Computational Mathematics and Modeling 1 Computational Mathematics and Mathematical Physics 1 Journal of Non-Newtonian Fluid Mechanics 1 SIAM Journal on Applied Mathematics ...and 35 more Serials
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### Cited in 39 Fields

 997 Numerical analysis (65-XX) 543 Partial differential equations (35-XX) 360 Fluid mechanics (76-XX) 145 Mechanics of deformable solids (74-XX) 27 Calculus of variations and optimal control; optimization (49-XX) 23 Biology and other natural sciences (92-XX) 21 Classical thermodynamics, heat transfer (80-XX) 16 Statistical mechanics, structure of matter (82-XX) 15 Optics, electromagnetic theory (78-XX) 12 Computer science (68-XX) 11 Ordinary differential equations (34-XX) 8 Probability theory and stochastic processes (60-XX) 7 Approximations and expansions (41-XX) 6 Geophysics (86-XX) 5 Real functions (26-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Operator theory (47-XX) 4 Statistics (62-XX) 4 Quantum theory (81-XX) 3 Potential theory (31-XX) 3 Special functions (33-XX) 3 Integral equations (45-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Operations research, mathematical programming (90-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Measure and integration (28-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Astronomy and astrophysics (85-XX)