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## Cai, Zhiqiang

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 Author ID: cai.zhiqiang Published as: Cai, Z.; Cai, Zhi-qiang; Cai, Zhiqiang; Chai, Zhiqiang
 Documents Indexed: 94 Publications since 1986
all top 5

#### Co-Authors

 5 single-authored 15 Zhang, Shun 14 McCormick, Steve Fahrney 9 Manteuffel, Thomas A. 7 Ye, Xiu 6 Kim, Seokchan 5 Douglas, Jim jun. 5 Ku, Jaeun 4 He, Cuiyu 4 Starke, Gerhard 3 Cai, Difeng 3 Dui, Hongyan 3 Si, Shubin 3 Sun, Shudong 3 Wang, Yanqiu 2 Cao, Shuhao 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 Zhang, Yingfeng 1 Attia, Frank S. 1 Bank, Randolph E. 1 Bertrand, Fleurianne 1 Bochev, Pavel B. 1 Carey, Varis 1 Chen, Binghe 1 E, Weinan 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, Rajčo D. 1 Lee, Barry 1 Lee, Hyung-Chun 1 Lin, Guang 1 Parashkevov, Rossen R. 1 Park, Eun-Jae 1 Park, Eunyoung 1 Parter, Seymour V. 1 Pasciak, Joseph E. 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 Tong, Charles Lai 1 Vassilevski, Panayot Spirov 1 Verfürth, Rüdiger 1 Wang, Junbo 1 Wang, Ning 1 Wang, Ping 1 Wilson, John David 1 Woo, Gyungsoo 1 Wu, Xiaohui 1 Xia, Jun 1 Zhang, Huilong 1 Zhang, Shuai 1 Zhao, Xibin
all top 5

#### Serials

 29 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 Mathematics of Computation 3 Communications in Statistics. Theory and Methods 3 Numerical Linear Algebra with Applications 2 Computers & Mathematics with Applications 2 Applied Mathematics and Computation 2 Calcolo 2 Numerische Mathematik 2 Journal of Scientific Computing 1 International Journal for Numerical Methods in Fluids 1 Hokkaido Mathematical Journal 1 Numerical Mathematics 1 Mathematica Numerica Sinica 1 Journal of Computational Mathematics 1 Applied Numerical Mathematics 1 Communications in Applied Numerical Methods 1 International Journal of High Speed Computing 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Mathematical Problems in Engineering 1 Journal of Ningxia University. Natural Science Edition 1 Computational Geosciences 1 Computational Methods in Applied Mathematics 1 Oberwolfach Reports
all top 5

#### Fields

 66 Numerical analysis (65-XX) 41 Partial differential equations (35-XX) 24 Fluid mechanics (76-XX) 16 Mechanics of deformable solids (74-XX) 4 Probability theory and stochastic processes (60-XX) 4 Operations research, mathematical programming (90-XX) 3 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

72 Publications have been cited 1,661 times in 1,060 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
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
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
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
Control-volume mixed finite element methods. Zbl 0941.76050
Cai, Z.; Jones, J. E.; McCormick, S. F.; Russell, T. F.
1997
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
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
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
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 the stress-displacement formulation: Linear elasticity. Zbl 1063.74099
Cai, Zhiqiang; Starke, Gerhard
2003
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
Robust adaptive asymptotic tracking of nonlinear systems with additive disturbance. Zbl 1366.93565
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
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
A sufficiently smooth projection operator. Zbl 1366.93283
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
2006
Mixed finite element methods for incompressible flow: stationary Navier-Stokes equations. Zbl 1410.76160
Cai, Zhiqiang; Wang, Chunbo; Zhang, Shun
2010
An adaptive mixed least-squares finite element method for viscoelastic fluids of Oldroyd type. Zbl 1274.76246
Cai, Z.; Westphal, C. R.
2009
Multigrid methods for nearly singular linear equations and eigenvalue problems. Zbl 0873.65030
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
1997
Robust equilibrated residual error estimator for diffusion problems: conforming elements. Zbl 1253.65175
Cai, Zhiqiang; Zhang, Shun
2012
The $$L^2$$ norm error estimates for the div least-squares method. Zbl 1138.76053
Cai, Zhiqiang; Ku, Jaeun
2006
Flux recovery and a posteriori error estimators: conforming elements for scalar elliptic equations. Zbl 1230.65117
Cai, Zhiqiang; Zhang, Shun
2010
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
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
Multilevel iteration for mixed finite element systems with penalty. Zbl 0809.65114
Cai, Zhiqiang; Goldstein, Charles I.; Pasciak, Joseph E.
1993
A mixed nonconforming finite element for linear elasticity. Zbl 1076.74053
Cai, Zhiqiang; Ye, Xiu
2005
Solution methods for the Poisson equation with corner singularities: Numerical results. Zbl 0991.65117
Cai, Zhiqiang; Kim, Seokchan; Shin, Byeong-Chun
2001
Recovery-based error estimator for stabilized finite element methods for the Stokes equation. Zbl 1296.76087
Song, Lina; Hou, Yanren; Cai, Zhiqiang
2014
A weighted $$H$$(div) least-squares method for second-order elliptic problems. Zbl 1168.65069
Cai, Z.; Westphal, C. R.
2008
Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. Zbl 1307.76050
Cai, Zhiqiang; Zhang, Shun
2012
Pseudostress-velocity formulation for incompressible Navier-Stokes equations. Zbl 1352.76043
Cai, Zhiqiang; Wang, Yanqiu
2010
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
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
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
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
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
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
Least-squares finite element approximations for the Reissner-Mindlin plate. Zbl 0982.74062
Chai, Zhiqiang; Ye, Xiu; Zhang, Huilong
1999
An error estimate for two-dimensional Stokes driven cavity flow. Zbl 1198.65217
Cai, Zhiqiang; Wang, Yanqiu
2009
A least-squares finite element approximation for the compressible Stokes equations. Zbl 0965.76039
Cai, Zhiqiang; Ye, Xiu
2000
Goal-oriented local a posteriori error estimators for $$H(\text{div})$$ least-squares finite element methods. Zbl 1298.65147
Cai, Zhiqiang; Ku, JaEun
2011
Improved ZZ a posteriori error estimators for diffusion problems: conforming linear elements. Zbl 1439.65153
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
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
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
Robust equilibrated error estimator for diffusion problems: mixed finite elements in two dimensions. Zbl 1437.65177
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
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
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
The discrete first-order system least squares: The second-order elliptic boundary value problem. Zbl 1017.65092
Cai, Zhiqiang; Shin, Byeong Chun
2002
Least squares for the perturbed Stokes equations and the Reissner–Mindlin plate. Zbl 1003.76047
Cai, Zhiqiang
2000
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
Joint integrated importance measure for multi-state transition systems. Zbl 1284.90018
Si, Shubin; Dui, Hongyan; Cai, Zhiqiang; Sun, Shudong; Zhang, Yingfeng
2012
A finite element method using singular functions for the Poisson equation: crack singularities. Zbl 1071.65152
Cai, Zhiqiang; Kim, Seokchan; Woo, Gyungsoo
2002
Uniform asymptotic analysis for transient waves in a pre-stressed compressible hyperelastic rod. Zbl 0982.74038
Dai, H.-H.; Cai, Z.
2000
Stabilized finite element methods with fast iterative solution algorithms for the Stokes problem. Zbl 0943.76048
Cai, Zhiqiang; Douglas, Jim jun.
1998
An analytic basis for multigrid methods for stabilized finite element methods for the Stokes problem. Zbl 0911.65124
Cai, Z.; Douglas, J. jun.
1997
Norm estimates of product operators with application to domain decomposition. Zbl 0766.65100
Cai, Zhiqiang
1993
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
Robust equilibrated error estimator for diffusion problems: mixed finite elements in two dimensions. Zbl 1437.65177
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
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
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
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
Improved ZZ a posteriori error estimators for diffusion problems: conforming linear elements. Zbl 1439.65153
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
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
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
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
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
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 1,391 Authors

 27 Cai, Zhiqiang 19 Yang, Suh-Yuh 19 Zou, Qingsong 17 Rui, Hongxing 17 Zhang, Zhimin 16 Bi, Chunjia 16 Cui, Junzhi 15 Luo, Zhendong 14 Chen, Zhangxin 14 Mu, Lin 14 Zhang, Shun 13 Manteuffel, Thomas A. 13 Ye, Xiu 12 Chen, Chuanjun 12 Chen, Yanping 12 Gatica, Gabriel N. 12 Li, Jian 12 Li, Yonghai 11 Ku, Jaeun 11 Shi, Dongyang 11 Yang, Min 11 Yuan, Yirang 10 Guo, Hui 10 He, Wenming 10 Kim, Sangdong 10 Li, Hong 10 Sheen, Dongwoo 10 Starke, Gerhard 9 Abdulle, Assyr 9 Hou, Thomas Yizhao 9 Kim, Seokchan 9 Lazarov, Raytcho D. 9 McCormick, Steve Fahrney 9 Ruiz-Baier, Ricardo 9 Vassilevski, Panayot Spirov 9 Wang, Junping 9 Xu, Jinchao 8 Cao, Liqun 8 Cao, Waixiang 8 Carstensen, Carsten 8 Feng, Xinlong 8 Lin, Yanping 8 Park, Eun-Jae 8 Zhang, Tie 8 Zhang, Zhiyue 7 He, Yinnian 7 Lee, Eunjung 7 Lee, Hsueh-Chen 7 Mao, Shipeng 7 Oyarzúa, Ricardo 7 Schröder, Jörg 7 Schwarz, Alexander 7 Shin, Byeong Chun 7 Valentin, Frédéric 7 Wu, Jiming 6 Bertrand, Fleurianne 6 Chen, Shaochun 6 Choi, Hyung Jun 6 Dehghan Takht Fooladi, Mehdi 6 Deng, Weibing 6 Ginting, Victor 6 Guan, Xiaofei 6 Hessari, Peyman 6 Heys, Jeffrey J. 6 Hu, Jun 6 Huang, Yunqing 6 Li, Changfeng 6 Song, Lina 6 Xie, Xiaoping 6 Yang, Danping 6 Zabaras, Nicholas J. 5 Adler, James H. 5 Cangiani, Andrea 5 Chen, Huangxin 5 Chen, Jinru 5 Demkowicz, Leszek F. 5 Dong, Hao 5 Duan, Huoyuan 5 Fang, Zhichao 5 Gerritsma, Marc I. 5 Hajibeygi, Hadi 5 He, Cuiyu 5 Huang, Pengzhan 5 Jenny, Patrick 5 Jeon, Youngmok 5 Kumar, Sarvesh 5 Kwak, Do Young 5 Leng, Haitao 5 Li, Qin 5 Liu, Jinn-Liang 5 Lv, Junliang 5 Nordbotten, Jan Martin 5 Reddy, Junuthula Narasimha 5 Saad, Mazen 5 Shi, Zhongci 5 Sinha, Rajen Kumar 5 Wang, Yanqiu 5 Westphal, Chad R. 5 Wohlmuth, Barbara I. 5 Yang, Qing ...and 1,291 more Authors
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#### Cited in 132 Serials

 90 Journal of Computational and Applied Mathematics 80 Computer Methods in Applied Mechanics and Engineering 66 Computers & Mathematics with Applications 59 Journal of Computational Physics 57 Applied Numerical Mathematics 56 Applied Mathematics and Computation 49 Numerical Methods for Partial Differential Equations 49 Journal of Scientific Computing 40 Numerische Mathematik 37 SIAM Journal on Numerical Analysis 34 Mathematics of Computation 20 Advances in Computational Mathematics 17 International Journal for Numerical Methods in Engineering 16 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 16 SIAM Journal on Scientific Computing 16 Multiscale Modeling & Simulation 11 Journal of Mathematical Analysis and Applications 11 Mathematical Methods in the Applied Sciences 11 International Journal of Computer Mathematics 11 Numerical Linear Algebra with Applications 11 Computational Geosciences 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Numerical Functional Analysis and Optimization 9 Computing 9 Computational Methods in Applied Mathematics 9 Journal of Numerical Mathematics 8 Automatica 8 Mathematical Problems in Engineering 8 Science China. Mathematics 7 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 6 International Journal of Control 6 International Journal for Numerical Methods in Fluids 6 Applications of Mathematics 6 Numerical Algorithms 6 Applied Mathematical Modelling 6 Computing and Visualization in Science 5 BIT 5 Mathematics and Computers in Simulation 5 Nonlinear Dynamics 5 Abstract and Applied Analysis 4 Journal of the Franklin Institute 4 Calcolo 4 Computational Mechanics 4 Journal of Systems Science and Complexity 4 International Journal of Computational Methods 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 Foundations of Computational Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Applied Mathematics and Computing 3 Boletim da Sociedade Paranaense de Matemática. Terceira Série 3 Advances in Difference Equations 3 East Asian Journal on Applied Mathematics 2 Journal of Fluid Mechanics 2 Information Sciences 2 Mathematical and Computer Modelling 2 Science in China. Series A 2 Japan Journal of Industrial and Applied Mathematics 2 International Journal of Adaptive Control and Signal Processing 2 Journal of Elasticity 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 Honam Mathematical Journal 2 Journal of Applied Mathematics 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 Journal of the Korean Society for Industrial and Applied Mathematics 2 AMM. Applied Mathematics and Mechanics. (English Edition) 2 Electronic Research Archive 1 Acta Mechanica 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 Mathematical Physics 1 Wave Motion 1 Chaos, Solitons and Fractals 1 Siberian Mathematical Journal 1 Optimal Control Applications & Methods 1 Systems & Control Letters 1 Computer Aided Geometric Design 1 COMPEL 1 Applied Mathematics Letters 1 Computational Mathematics and Modeling 1 Computational Mathematics and Mathematical Physics 1 Journal of Non-Newtonian Fluid Mechanics 1 International Journal of Robust and Nonlinear Control 1 Applied Mathematics. Series B (English Edition) 1 Applied and Computational Harmonic Analysis 1 Computational and Applied Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Complexity 1 Discrete and Continuous Dynamical Systems 1 Mathematics and Mechanics of Solids ...and 32 more Serials
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#### Cited in 40 Fields

 870 Numerical analysis (65-XX) 488 Partial differential equations (35-XX) 318 Fluid mechanics (76-XX) 134 Mechanics of deformable solids (74-XX) 37 Systems theory; control (93-XX) 25 Calculus of variations and optimal control; optimization (49-XX) 21 Classical thermodynamics, heat transfer (80-XX) 20 Biology and other natural sciences (92-XX) 15 Statistical mechanics, structure of matter (82-XX) 13 Ordinary differential equations (34-XX) 13 Optics, electromagnetic theory (78-XX) 10 Probability theory and stochastic processes (60-XX) 6 Approximations and expansions (41-XX) 6 Geophysics (86-XX) 5 Mechanics of particles and systems (70-XX) 4 Real functions (26-XX) 4 Computer science (68-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Special functions (33-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Operator theory (47-XX) 3 Statistics (62-XX) 3 Quantum theory (81-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Potential theory (31-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)