×
Author ID: cai.zhiqiang Recent zbMATH articles by "Cai, Zhiqiang"
Published as: Cai, Zhiqiang; Cai, Z.; Cai, Zhi-qiang; Chai, Zhiqiang
all top 5

Co-Authors

6 single-authored
19 Zhang, Shun
14 McCormick, Steve Fahrney
10 Liu, Min
9 Manteuffel, Thomas A.
7 Ye, Xiu
6 Chen, Jingshuang
6 He, Cuiyu
6 Kim, Seokchan
5 Douglas, Jim jun.
5 Ku, Jaeun
4 Cai, Difeng
4 Si, Shubin
4 Starke, Gerhard
3 Cao, Shuhao
3 Dui, Hongyan
3 Park, Moongyu
3 Sun, Shudong
3 Wang, Yanqiu
2 Chen, Binghe
2 Choi, Junpyo
2 Dawson, Darren M.
2 de Queiroz, Marcio S.
2 Du, Shaohong
2 Falgout, Rob
2 Hao, Zhaopeng
2 Lee, Chang-Ock
2 Mandel, Jan
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 Baier, Stephan
1 Bank, Randolph E.
1 Baranov, M. A.
1 Bertrand, Fleurianne
1 Bochev, Pavel B.
1 Carey, Varis
1 Chomaz, L.
1 Du, Ding-Zhu
1 Duan, Dongli
1 E, Weinan
1 Falgout, Robert D.
1 Ferlaino, F.
1 Goldstein, Charles I.
1 Guo, Ben-Yu
1 Hejnal, Brooke
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, Baoliang
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 Ramani, Karthik
1 Ruge, J.
1 Santos, Juan Enrique
1 Saygin, Can
1 Shang, Lijun
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 Wang, Ping
1 Wilson, John David
1 Woo, Gyungsoo
1 Wu, Cang
1 Wu, Xiaohui
1 Xia, Jun
1 Zhang, Huilong
1 Zhang, Shuai
1 Zhang, Yang
1 Zhao, Xibin
1 Zoller, Peter
all top 5

Serials

30 SIAM Journal on Numerical Analysis
8 Computer Methods in Applied Mechanics and Engineering
6 Numerical Methods for Partial Differential Equations
5 Computers & Mathematics with Applications
5 SIAM Journal on Scientific Computing
4 Mathematics of Computation
3 Journal of Computational Physics
3 Applied Mathematics and Computation
3 Applied Numerical Mathematics
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 Journal of Computational and Applied Mathematics
2 Numerische Mathematik
1 Acta Mechanica
1 Classical and Quantum Gravity
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 Communications in Applied Numerical Methods
1 International Journal of High Speed Computing
1 Applied Mathematical Modelling
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
1 East Asian Journal on Applied Mathematics

Publications by Year

Citations contained in zbMATH Open

92 Publications have been cited 2,182 times in 1,357 Documents Cited by Year
On the finite volume element method. Zbl 0731.65093
Cai, Zhiqiang
233
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
215
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.
144
1994
The finite volume element method for diffusion equations on general triangulations. Zbl 0729.65086
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
123
1991
On the accuracy of the finite volume element method for diffusion equations on composite grids. Zbl 0707.65073
Cai, Zhiqiang; McCormick, Steve
91
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.
86
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
79
2011
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.
76
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
57
1999
Least-squares methods for incompressible Newtonian fluid flow: linear stationary problems. Zbl 1159.76347
Cai, Zhiqiang; Lee, Barry; Wang, Ping
57
2004
Least-squares methods for linear elasticity. Zbl 1159.74419
Cai, Zhiqiang; Starke, Gerhard
56
2004
Recovery-based error estimator for interface problems: Conforming linear elements. Zbl 1204.65129
Cai, Zhiqiang; Zhang, Shun
53
2009
Control-volume mixed finite element methods. Zbl 0941.76050
Cai, Z.; Jones, J. E.; McCormick, S. F.; Russell, T. F.
50
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.
48
1998
A finite element method using singular functions for the Poisson equation: Corner singularities. Zbl 0992.65122
Cai, Zhiqiang; Kim, Seokchan
43
2001
Mixed finite element methods for incompressible flow: stationary Stokes equations. Zbl 1267.76059
Cai, Zhiqiang; Tong, Charles; Vassilevski, Panayot S.; Wang, Chunbo
43
2010
Development and analysis of higher order finite volume methods over rectangles for elliptic equations. Zbl 1020.65087
Cai, Zhiqiang; Douglas, Jim jun.; Park, Moongyu
40
2003
Recovery-based error estimators for interface problems: mixed and nonconforming finite elements. Zbl 1210.65185
Cai, Zhiqiang; Zhang, Shun
35
2010
First-order system least squares for the stress-displacement formulation: Linear elasticity. Zbl 1063.74099
Cai, Zhiqiang; Starke, Gerhard
33
2003
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs. Zbl 07506625
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min; Liu, Xinyu
31
2020
Robust adaptive asymptotic tracking of nonlinear systems with additive disturbance. Zbl 1366.93565
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
29
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
29
2017
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.
28
1995
Robust equilibrated residual error estimator for diffusion problems: conforming elements. Zbl 1253.65175
Cai, Zhiqiang; Zhang, Shun
26
2012
A sufficiently smooth projection operator. Zbl 1366.93283
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
26
2006
Nonconforming quadrilateral finite elements: a correction. Zbl 1012.65124
Cai, Z.; Douglas, J. jun.; Santos, J. E.; Sheen, D.; Ye, X.
25
2000
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.
23
2001
A multigrid method for the pseudostress formulation of Stokes problems. Zbl 1182.76896
Cai, Zhiqiang; Wang, Yanqiu
22
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.
21
1998
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
21
2005
Mixed finite element methods for incompressible flow: stationary Navier-Stokes equations. Zbl 1410.76160
Cai, Zhiqiang; Wang, Chunbo; Zhang, Shun
20
2010
Flux recovery and a posteriori error estimators: conforming elements for scalar elliptic equations. Zbl 1230.65117
Cai, Zhiqiang; Zhang, Shun
20
2010
An adaptive mixed least-squares finite element method for viscoelastic fluids of Oldroyd type. Zbl 1274.76246
Cai, Z.; Westphal, C. R.
20
2009
The \(L^2\) norm error estimates for the div least-squares method. Zbl 1138.76053
Cai, Zhiqiang; Ku, Jaeun
18
2006
Multigrid methods for nearly singular linear equations and eigenvalue problems. Zbl 0873.65030
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
17
1997
Solution methods for the Poisson equation with corner singularities: Numerical results. Zbl 0991.65117
Cai, Zhiqiang; Kim, Seokchan; Shin, Byeong-Chun
16
2001
Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. Zbl 1307.76050
Cai, Zhiqiang; Zhang, Shun
16
2012
A mixed nonconforming finite element for linear elasticity. Zbl 1076.74053
Cai, Zhiqiang; Ye, Xiu
15
2005
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
15
2019
A finite element method using singular functions for Poisson equations: Mixed boundary conditions. Zbl 1124.65108
Cai, Zhiqiang; Kim, Seokchan; Kim, Sangdong; Kong, Sooryun
14
2006
Multilevel iteration for mixed finite element systems with penalty. Zbl 0809.65114
Cai, Zhiqiang; Goldstein, Charles I.; Pasciak, Joseph E.
14
1993
A recovery-based a posteriori error estimator for \(H\)(curl) interface problems. Zbl 1425.65153
Cai, Zhiqiang; Cao, Shuhao
12
2015
Pseudostress-velocity formulation for incompressible Navier-Stokes equations. Zbl 1352.76043
Cai, Zhiqiang; Wang, Yanqiu
11
2010
A weighted \(H\)(div) least-squares method for second-order elliptic problems. Zbl 1168.65069
Cai, Z.; Westphal, C. R.
11
2008
Recovery-based error estimator for stabilized finite element methods for the Stokes equation. Zbl 1296.76087
Song, Lina; Hou, Yanren; Cai, Zhiqiang
11
2014
Analysis of epidemic vaccination strategies on heterogeneous networks: based on SEIRV model and evolutionary game. Zbl 1510.92223
Meng, Xueyu; Cai, Zhiqiang; Si, Shubin; Duan, Dongli
11
2021
Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation. Zbl 07515414
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
11
2021
Residual-based a posteriori error estimate for interface problems: nonconforming linear elements. Zbl 1355.65145
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
10
2017
Div first-order system LL* (FOSLL*) for second-order elliptic partial differential equations. Zbl 1312.65005
Cai, Zhiqiang; Falgout, Rob; Zhang, Shun
10
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.
9
2000
Improved ZZ a posteriori error estimators for diffusion problems: conforming linear elements. Zbl 1439.65153
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
9
2017
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
8
2010
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.
8
2000
Least-squares finite element approximations for the Reissner-Mindlin plate. Zbl 0982.74062
Chai, Zhiqiang; Ye, Xiu; Zhang, Huilong
8
1999
Adaptive two-layer ReLU neural network. I: Best least-squares approximation. Zbl 1504.65275
Liu, Min; Cai, Zhiqiang; Chen, Jingshuang
8
2022
An error estimate for two-dimensional Stokes driven cavity flow. Zbl 1198.65217
Cai, Zhiqiang; Wang, Yanqiu
7
2009
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.
6
2016
A dual finite element method for a singularly perturbed reaction-diffusion problem. Zbl 1440.65188
Cai, Zhiqiang; Ku, JaEun
6
2020
Least squares for the perturbed Stokes equations and the Reissner–Mindlin plate. Zbl 1003.76047
Cai, Zhiqiang
5
2000
A least-squares finite element approximation for the compressible Stokes equations. Zbl 0965.76039
Cai, Zhiqiang; Ye, Xiu
5
2000
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.
5
2003
Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Zbl 1447.65130
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
5
2020
Adaptive two-layer ReLU neural network. II: Ritz approximation to elliptic PDEs. Zbl 1524.65939
Liu, Min; Cai, Zhiqiang
5
2022
Goal-oriented local a posteriori error estimators for \(H(\text{div})\) least-squares finite element methods. Zbl 1298.65147
Cai, Zhiqiang; Ku, JaEun
4
2011
Robust residual- and recovery-based a posteriori error estimators for interface problems with flux jumps. Zbl 1245.65148
Cai, Zhiqiang; Zhang, Shun
4
2012
Least-squares method for the Oseen equation. Zbl 1407.76026
Cai, Zhiqiang; Chen, Binghe
4
2016
Least-squares methods for elasticity and Stokes equations with weakly imposed symmetry. Zbl 1420.65115
Bertrand, Fleurianne; Cai, Zhiqiang; Park, Eun Young
4
2019
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
4
2015
First-order system least squares for the Signorini contact problem in linear elasticity. Zbl 1410.74058
Attia, Frank S.; Cai, Zhiqiang; Starke, Gerhard
4
2009
A hybrid a posteriori error estimator for conforming finite element approximations. Zbl 1440.65187
Cai, Difeng; Cai, Zhiqiang
4
2018
Robust equilibrated error estimator for diffusion problems: mixed finite elements in two dimensions. Zbl 1437.65177
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
4
2020
Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements. Zbl 1478.65116
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
4
2021
A finite element method using singular functions: interface problems. Zbl 1140.65084
Kim, Seokchan; Cai, Zhiqiang; Pyo, Jae-Hong; Kong, Sooryoun
3
2007
Improved ZZ a posteriori error estimators for diffusion problems: discontinuous elements. Zbl 1460.65143
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
3
2021
Robust a posteriori error estimation for finite element approximation to \(\boldsymbol{H}(\mathbf{curl})\) problem. Zbl 1439.78019
Cai, Zhiqiang; Cao, Shuhao; Falgout, Rob
3
2016
Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law. Zbl 1484.65174
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
3
2022
The discrete first-order system least squares: The second-order elliptic boundary value problem. Zbl 1017.65092
Cai, Zhiqiang; Shin, Byeong Chun
2
2002
Analytic spectra of CMB anisotropies and polarization generated by scalar perturbations in synchronous gauge. Zbl 1242.85011
Cai, Z.; Zhang, Y.
2
2012
Self-adaptive deep neural network: numerical approximation to functions and PDEs. Zbl 07518092
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
2
2022
Error estimate of a finite element method using stress intensity factor. Zbl 1442.65348
Cai, Zhiqiang; Kim, Seokchan; Lee, Hyung-Chun
2
2018
Error estimates for a Schwarz alternating procedure on L-shaped regions. Zbl 0655.65113
Cai, Zhiqiang; Guo, Benju
1
1988
Uniform asymptotic analysis for transient waves in a pre-stressed compressible hyperelastic rod. Zbl 0982.74038
Dai, H.-H.; Cai, Z.
1
2000
An analytic basis for multigrid methods for stabilized finite element methods for the Stokes problem. Zbl 0911.65124
Cai, Z.; Douglas, J. jun.
1
1997
A finite element method using singular functions for the Poisson equation: crack singularities. Zbl 1071.65152
Cai, Zhiqiang; Kim, Seokchan; Woo, Gyungsoo
1
2002
Convergence estimates of multilevel additive and multiplicative algorithms for non-symmetric and indefinite problems. Zbl 0852.65112
Cai, Zhiqiang; Lai, Chen-Yao G.
1
1996
Stabilized finite element methods with fast iterative solution algorithms for the Stokes problem. Zbl 0943.76048
Cai, Zhiqiang; Douglas, Jim jun.
1
1998
Computational complexity of the Schwarz alternating procedure. Zbl 0726.65029
Cai, Zhiqiang; McCormick, Steve
1
1989
Norm estimates of product operators with application to domain decomposition. Zbl 0766.65100
Cai, Zhiqiang
1
1993
Joint integrated importance measure for multi-state transition systems. Zbl 1284.90018
Si, Shubin; Dui, Hongyan; Cai, Zhiqiang; Sun, Shudong; Zhang, Yingfeng
1
2012
A hidden semi-Markov model with duration-dependent state transition probabilities for prognostics. Zbl 1407.90336
Wang, Ning; Sun, Shu-dong; Cai, Zhi-qiang; Zhang, Shuai; Saygin, Can
1
2014
A finite element method for Dirichlet boundary control of elliptic partial differential equations. Zbl 1486.49032
Du, Shaohong; Cai, Zhiqiang
1
2022
Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: discrete divergence operator. Zbl 07715661
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
1
2023
Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: discrete divergence operator. Zbl 07715661
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
1
2023
Adaptive two-layer ReLU neural network. I: Best least-squares approximation. Zbl 1504.65275
Liu, Min; Cai, Zhiqiang; Chen, Jingshuang
8
2022
Adaptive two-layer ReLU neural network. II: Ritz approximation to elliptic PDEs. Zbl 1524.65939
Liu, Min; Cai, Zhiqiang
5
2022
Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law. Zbl 1484.65174
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
3
2022
Self-adaptive deep neural network: numerical approximation to functions and PDEs. Zbl 07518092
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
2
2022
A finite element method for Dirichlet boundary control of elliptic partial differential equations. Zbl 1486.49032
Du, Shaohong; Cai, Zhiqiang
1
2022
Analysis of epidemic vaccination strategies on heterogeneous networks: based on SEIRV model and evolutionary game. Zbl 1510.92223
Meng, Xueyu; Cai, Zhiqiang; Si, Shubin; Duan, Dongli
11
2021
Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation. Zbl 07515414
Cai, Zhiqiang; Chen, Jingshuang; Liu, Min
11
2021
Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements. Zbl 1478.65116
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
4
2021
Improved ZZ a posteriori error estimators for diffusion problems: discontinuous elements. Zbl 1460.65143
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
3
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
31
2020
A dual finite element method for a singularly perturbed reaction-diffusion problem. Zbl 1440.65188
Cai, Zhiqiang; Ku, JaEun
6
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
5
2020
Robust equilibrated error estimator for diffusion problems: mixed finite elements in two dimensions. Zbl 1437.65177
Cai, Difeng; Cai, Zhiqiang; Zhang, Shun
4
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
15
2019
Least-squares methods for elasticity and Stokes equations with weakly imposed symmetry. Zbl 1420.65115
Bertrand, Fleurianne; Cai, Zhiqiang; Park, Eun Young
4
2019
A hybrid a posteriori error estimator for conforming finite element approximations. Zbl 1440.65187
Cai, Difeng; Cai, Zhiqiang
4
2018
Error estimate of a finite element method using stress intensity factor. Zbl 1442.65348
Cai, Zhiqiang; Kim, Seokchan; Lee, Hyung-Chun
2
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
29
2017
Residual-based a posteriori error estimate for interface problems: nonconforming linear elements. Zbl 1355.65145
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
10
2017
Improved ZZ a posteriori error estimators for diffusion problems: conforming linear elements. Zbl 1439.65153
Cai, Zhiqiang; He, Cuiyu; Zhang, Shun
9
2017
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.
6
2016
Least-squares method for the Oseen equation. Zbl 1407.76026
Cai, Zhiqiang; Chen, Binghe
4
2016
Robust a posteriori error estimation for finite element approximation to \(\boldsymbol{H}(\mathbf{curl})\) problem. Zbl 1439.78019
Cai, Zhiqiang; Cao, Shuhao; Falgout, Rob
3
2016
A recovery-based a posteriori error estimator for \(H\)(curl) interface problems. Zbl 1425.65153
Cai, Zhiqiang; Cao, Shuhao
12
2015
Div first-order system LL* (FOSLL*) for second-order elliptic partial differential equations. Zbl 1312.65005
Cai, Zhiqiang; Falgout, Rob; Zhang, Shun
10
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
4
2015
Recovery-based error estimator for stabilized finite element methods for the Stokes equation. Zbl 1296.76087
Song, Lina; Hou, Yanren; Cai, Zhiqiang
11
2014
A hidden semi-Markov model with duration-dependent state transition probabilities for prognostics. Zbl 1407.90336
Wang, Ning; Sun, Shu-dong; Cai, Zhi-qiang; Zhang, Shuai; Saygin, Can
1
2014
Robust equilibrated residual error estimator for diffusion problems: conforming elements. Zbl 1253.65175
Cai, Zhiqiang; Zhang, Shun
26
2012
Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. Zbl 1307.76050
Cai, Zhiqiang; Zhang, Shun
16
2012
Robust residual- and recovery-based a posteriori error estimators for interface problems with flux jumps. Zbl 1245.65148
Cai, Zhiqiang; Zhang, Shun
4
2012
Analytic spectra of CMB anisotropies and polarization generated by scalar perturbations in synchronous gauge. Zbl 1242.85011
Cai, Z.; Zhang, Y.
2
2012
Joint integrated importance measure for multi-state transition systems. Zbl 1284.90018
Si, Shubin; Dui, Hongyan; Cai, Zhiqiang; Sun, Shudong; Zhang, Yingfeng
1
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
79
2011
Goal-oriented local a posteriori error estimators for \(H(\text{div})\) least-squares finite element methods. Zbl 1298.65147
Cai, Zhiqiang; Ku, JaEun
4
2011
Mixed finite element methods for incompressible flow: stationary Stokes equations. Zbl 1267.76059
Cai, Zhiqiang; Tong, Charles; Vassilevski, Panayot S.; Wang, Chunbo
43
2010
Recovery-based error estimators for interface problems: mixed and nonconforming finite elements. Zbl 1210.65185
Cai, Zhiqiang; Zhang, Shun
35
2010
Mixed finite element methods for incompressible flow: stationary Navier-Stokes equations. Zbl 1410.76160
Cai, Zhiqiang; Wang, Chunbo; Zhang, Shun
20
2010
Flux recovery and a posteriori error estimators: conforming elements for scalar elliptic equations. Zbl 1230.65117
Cai, Zhiqiang; Zhang, Shun
20
2010
Pseudostress-velocity formulation for incompressible Navier-Stokes equations. Zbl 1352.76043
Cai, Zhiqiang; Wang, Yanqiu
11
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
8
2010
Recovery-based error estimator for interface problems: Conforming linear elements. Zbl 1204.65129
Cai, Zhiqiang; Zhang, Shun
53
2009
An adaptive mixed least-squares finite element method for viscoelastic fluids of Oldroyd type. Zbl 1274.76246
Cai, Z.; Westphal, C. R.
20
2009
An error estimate for two-dimensional Stokes driven cavity flow. Zbl 1198.65217
Cai, Zhiqiang; Wang, Yanqiu
7
2009
First-order system least squares for the Signorini contact problem in linear elasticity. Zbl 1410.74058
Attia, Frank S.; Cai, Zhiqiang; Starke, Gerhard
4
2009
A weighted \(H\)(div) least-squares method for second-order elliptic problems. Zbl 1168.65069
Cai, Z.; Westphal, C. R.
11
2008
A multigrid method for the pseudostress formulation of Stokes problems. Zbl 1182.76896
Cai, Zhiqiang; Wang, Yanqiu
22
2007
A finite element method using singular functions: interface problems. Zbl 1140.65084
Kim, Seokchan; Cai, Zhiqiang; Pyo, Jae-Hong; Kong, Sooryoun
3
2007
Robust adaptive asymptotic tracking of nonlinear systems with additive disturbance. Zbl 1366.93565
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
29
2006
A sufficiently smooth projection operator. Zbl 1366.93283
Cai, Z.; de Queiroz, M. S.; Dawson, D. M.
26
2006
The \(L^2\) norm error estimates for the div least-squares method. Zbl 1138.76053
Cai, Zhiqiang; Ku, Jaeun
18
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
14
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
21
2005
A mixed nonconforming finite element for linear elasticity. Zbl 1076.74053
Cai, Zhiqiang; Ye, Xiu
15
2005
Least-squares methods for incompressible Newtonian fluid flow: linear stationary problems. Zbl 1159.76347
Cai, Zhiqiang; Lee, Barry; Wang, Ping
57
2004
Least-squares methods for linear elasticity. Zbl 1159.74419
Cai, Zhiqiang; Starke, Gerhard
56
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
40
2003
First-order system least squares for the stress-displacement formulation: Linear elasticity. Zbl 1063.74099
Cai, Zhiqiang; Starke, Gerhard
33
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.
5
2003
The discrete first-order system least squares: The second-order elliptic boundary value problem. Zbl 1017.65092
Cai, Zhiqiang; Shin, Byeong Chun
2
2002
A finite element method using singular functions for the Poisson equation: crack singularities. Zbl 1071.65152
Cai, Zhiqiang; Kim, Seokchan; Woo, Gyungsoo
1
2002
A finite element method using singular functions for the Poisson equation: Corner singularities. Zbl 0992.65122
Cai, Zhiqiang; Kim, Seokchan
43
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.
23
2001
Solution methods for the Poisson equation with corner singularities: Numerical results. Zbl 0991.65117
Cai, Zhiqiang; Kim, Seokchan; Shin, Byeong-Chun
16
2001
Nonconforming quadrilateral finite elements: a correction. Zbl 1012.65124
Cai, Z.; Douglas, J. jun.; Santos, J. E.; Sheen, D.; Ye, X.
25
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.
9
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.
8
2000
Least squares for the perturbed Stokes equations and the Reissner–Mindlin plate. Zbl 1003.76047
Cai, Zhiqiang
5
2000
A least-squares finite element approximation for the compressible Stokes equations. Zbl 0965.76039
Cai, Zhiqiang; Ye, Xiu
5
2000
Uniform asymptotic analysis for transient waves in a pre-stressed compressible hyperelastic rod. Zbl 0982.74038
Dai, H.-H.; Cai, Z.
1
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
215
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
57
1999
Least-squares finite element approximations for the Reissner-Mindlin plate. Zbl 0982.74062
Chai, Zhiqiang; Ye, Xiu; Zhang, Huilong
8
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.
48
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.
21
1998
Stabilized finite element methods with fast iterative solution algorithms for the Stokes problem. Zbl 0943.76048
Cai, Zhiqiang; Douglas, Jim jun.
1
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.
86
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.
76
1997
Control-volume mixed finite element methods. Zbl 0941.76050
Cai, Z.; Jones, J. E.; McCormick, S. F.; Russell, T. F.
50
1997
Multigrid methods for nearly singular linear equations and eigenvalue problems. Zbl 0873.65030
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
17
1997
An analytic basis for multigrid methods for stabilized finite element methods for the Stokes problem. Zbl 0911.65124
Cai, Z.; Douglas, J. jun.
1
1997
Convergence estimates of multilevel additive and multiplicative algorithms for non-symmetric and indefinite problems. Zbl 0852.65112
Cai, Zhiqiang; Lai, Chen-Yao G.
1
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.
28
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.
144
1994
Multilevel iteration for mixed finite element systems with penalty. Zbl 0809.65114
Cai, Zhiqiang; Goldstein, Charles I.; Pasciak, Joseph E.
14
1993
Norm estimates of product operators with application to domain decomposition. Zbl 0766.65100
Cai, Zhiqiang
1
1993
On the finite volume element method. Zbl 0731.65093
Cai, Zhiqiang
233
1991
The finite volume element method for diffusion equations on general triangulations. Zbl 0729.65086
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
123
1991
On the accuracy of the finite volume element method for diffusion equations on composite grids. Zbl 0707.65073
Cai, Zhiqiang; McCormick, Steve
91
1990
Computational complexity of the Schwarz alternating procedure. Zbl 0726.65029
Cai, Zhiqiang; McCormick, Steve
1
1989
Error estimates for a Schwarz alternating procedure on L-shaped regions. Zbl 0655.65113
Cai, Zhiqiang; Guo, Benju
1
1988
all top 5

Cited by 1,635 Authors

41 Cai, Zhiqiang
22 Zou, Qingsong
21 Zhang, Zhimin
20 Li, Yonghai
20 Zhang, Shun
19 Yang, Suh-Yuh
18 Chen, Chuanjun
18 Rui, Hongxing
18 Yuan, Yirang
17 Cui, Junzhi
16 Bi, Chunjia
16 Luo, Zhendong
16 Mu, Lin
16 Ye, Xiu
15 Chen, Zhangxin
14 Chen, Yanping
14 Li, Jian
14 Starke, Gerhard
13 Bertrand, Fleurianne
13 Li, Changfeng
13 Shi, Dongyang
12 Gatica, Gabriel N.
12 He, Cuiyu
12 Kim, Seokchan
12 Ku, Jaeun
12 Lee, Eunjung
12 Manteuffel, Thomas A.
12 Park, Eun-Jae
12 Schröder, Jörg
12 Yang, Min
11 Carstensen, Carsten
11 Feng, Xinlong
11 Huang, Yunqing
11 Sheen, Dongwoo
11 Vassilevski, Panayot Spirov
10 Abdulle, Assyr
10 Cao, Waixiang
10 Guo, Hui
10 He, Wenming
10 Hou, Thomas Yizhao
10 Kim, Sangdong
10 Li, Hong
10 Ruiz-Baier, Ricardo
10 Schwarz, Alexander
10 Wang, Junping
10 Wu, Jiming
10 Zhang, Zhiyue
9 Chen, Jinru
9 Lazarov, Raytcho D.
9 Valentin, Frédéric
9 Xu, Jinchao
9 Zhou, Yanhui
8 Cao, Liqun
8 Demkowicz, Leszek F.
8 Deng, Weibing
8 Guan, Xiaofei
8 Hu, Jun
8 Lin, Yanping
8 Liu, Min
8 Liu, Wei
8 McCormick, Steve Fahrney
8 Oyarzúa, Ricardo
8 Song, Huailing
8 Zhang, Tie
8 Zhang, Zhiwen
7 Cangiani, Andrea
7 Cao, Shuhao
7 Dehghan Takht Fooladi, Mehdi
7 Lee, Hsueh-Chen
7 Mao, Shipeng
7 Shin, Byeong Chun
7 Wang, Xiang
7 Xie, Xiaoping
7 Yang, Qing
7 Zhang, Xu
6 Adler, James H.
6 Bringmann, Philipp
6 Chen, Jingshuang
6 Chen, Shaochun
6 Choi, Hyungjun
6 Dong, Hao
6 Duan, Huoyuan
6 Führer, Thomas
6 Gerritsma, Marc I.
6 Ginting, Victor
6 He, Yinnian
6 Hessari, Peyman
6 Huang, Pengzhan
6 Kumar, Sarvesh
6 Kwak, Do Young
6 Li, Minghao
6 Li, Qin
6 Luo, Zhongxuan
6 Lv, Junliang
6 Meng, Zhaoliang
6 Mora, David
6 Saad, Mazen
6 Sinha, Rajen Kumar
6 Song, Lina
6 Wang, Hong
...and 1,535 more Authors
all top 5

Cited in 152 Serials

107 Journal of Computational and Applied Mathematics
101 Computers & Mathematics with Applications
100 Computer Methods in Applied Mechanics and Engineering
80 Journal of Computational Physics
72 Journal of Scientific Computing
67 Applied Numerical Mathematics
65 Numerical Methods for Partial Differential Equations
62 Applied Mathematics and Computation
44 Numerische Mathematik
41 SIAM Journal on Numerical Analysis
35 Mathematics of Computation
22 SIAM Journal on Scientific Computing
22 Advances in Computational Mathematics
22 Multiscale Modeling & Simulation
19 International Journal for Numerical Methods in Engineering
19 International Journal of Computer Mathematics
19 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
18 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
15 Advances in Applied Mathematics and Mechanics
13 Mathematical Methods in the Applied Sciences
13 Computational Methods in Applied Mathematics
11 Journal of Mathematical Analysis and Applications
11 Numerical Algorithms
11 Numerical Linear Algebra with Applications
11 Computational Geosciences
10 Numerical Functional Analysis and Optimization
10 Journal of Numerical Mathematics
10 International Journal of Numerical Analysis and Modeling
10 Communications in Computational Physics
9 Computing
9 Science China. Mathematics
8 Calcolo
7 Computing and Visualization in Science
7 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
7 East Asian Journal on Applied Mathematics
6 International Journal for Numerical Methods in Fluids
6 BIT
6 Journal of Computational Mathematics
6 Computational Mechanics
6 Applications of Mathematics
6 Applied Mathematical Modelling
6 Mathematical Problems in Engineering
5 Mathematics and Computers in Simulation
5 Abstract and Applied Analysis
5 Journal of Applied Mathematics and Computing
5 International Journal of Computational Methods
4 Acta Mathematicae Applicatae Sinica. English Series
4 Foundations of Computational Mathematics
4 Journal of Systems Science and Complexity
4 Electronic Research Archive
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 Communications in Numerical Methods in Engineering
3 Computational and Applied Mathematics
3 ETNA. Electronic Transactions on Numerical Analysis
3 Engineering Analysis with Boundary Elements
3 Journal of Inequalities and Applications
3 Discrete and Continuous Dynamical Systems. Series B
3 Acta Mathematica Scientia. Series B. (English Edition)
3 Boletim da Sociedade Paranaense de Matemática. Terceira Série
3 Advances in Difference Equations
3 East Asian Mathematical Journal
3 Journal of the Korean Society for Industrial and Applied Mathematics
2 Acta Mechanica
2 Journal of Fluid Mechanics
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 Applied and Computational Harmonic Analysis
2 International Journal of Computational Fluid Dynamics
2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
2 Honam Mathematical Journal
2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
2 Communications in Nonlinear Science and Numerical Simulation
2 Journal of Applied Mathematics
2 Communications on Pure and Applied Analysis
2 Central European Journal of Mathematics
2 Acta Numerica
2 GAMM-Mitteilungen
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 Mathematics
2 AMM. Applied Mathematics and Mechanics. (English Edition)
2 AIMS Mathematics
2 SMAI Journal of Computational Mathematics
2 Communications on Applied Mathematics and Computation
2 International Journal on Finite Volumes
1 Computers and Fluids
1 Computer Physics Communications
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
...and 52 more Serials
all top 5

Cited in 39 Fields

1,179 Numerical analysis (65-XX)
676 Partial differential equations (35-XX)
397 Fluid mechanics (76-XX)
184 Mechanics of deformable solids (74-XX)
37 Calculus of variations and optimal control; optimization (49-XX)
32 Computer science (68-XX)
32 Biology and other natural sciences (92-XX)
24 Classical thermodynamics, heat transfer (80-XX)
23 Optics, electromagnetic theory (78-XX)
19 Statistical mechanics, structure of matter (82-XX)
16 Ordinary differential equations (34-XX)
15 Approximations and expansions (41-XX)
12 Probability theory and stochastic processes (60-XX)
8 Real functions (26-XX)
6 Potential theory (31-XX)
5 Integral equations (45-XX)
5 Global analysis, analysis on manifolds (58-XX)
5 Statistics (62-XX)
5 Geophysics (86-XX)
4 Linear and multilinear algebra; matrix theory (15-XX)
4 Special functions (33-XX)
4 Operator theory (47-XX)
4 Quantum theory (81-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
3 Functional analysis (46-XX)
3 Operations research, mathematical programming (90-XX)
3 Systems theory; control (93-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 Mechanics of particles and systems (70-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 Astronomy and astrophysics (85-XX)

Citations by Year