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## Shi, Zhongci

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 Author ID: shi.zhongci Published as: Shi, Zhongci; Shi, Zhong-Ci; Shi, Zhong-ci; Shih, C. T.; Shi, Z. C.; Shi, Z.-C.; Shi, Zhong Ci; Shi, Z.; Shih, Chung-tze; Shi, ZhongCi; Zhong-ci Homepage: http://icmsec.cc.ac.cn/staff/shi.html External Links: Wikidata · dblp
 Documents Indexed: 172 Publications since 1964, including 17 Books Biographic References: 3 Publications
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#### Co-Authors

 31 single-authored 21 Hu, Jun 20 Ming, Pingbing 19 Xu, Xuejun 12 Mao, Shipeng 7 Chen, Shaochun 7 Huang, Jianguo 7 Zhao, Xuying 6 Xie, Zhenghui 4 Feng, Kang 3 Guo, Ling 3 Man, Hongying 3 Shi, Dongyang 3 Wang, Ming 3 Xu, Jinchao 3 Yi, Xuexi 2 Becker, Roland 2 Chen, Chuanmiao 2 Chen, Zhangxin 2 Huang, Yunqing 2 Jiang, Bin 2 Lai, Junjiang 2 Li, Hongliang 2 Li, Yishen 2 Nicaise, Serge 2 Okamoto, Hisashi 2 Pittenger, Arthur O. 2 Sheen, Dongwoo 2 Tang, Tao 2 Wang, Jiacheng 2 Wang, Lin-Cheng 2 Xu, Yifeng 2 Xu, Yun 2 Xue, Weimin 2 Yu, Dehao 2 Zhang, Fei 2 Zhang, Zhimin 1 Bai, Zhongzhi 1 Braess, Dietrich 1 Chan, Cheong-ki K. 1 Chan, Tony Fan-Cheong 1 Chen, Jinru 1 Chen, Qianyong 1 Chen, Xiaojun 1 Chen, Zhiming 1 Du, Qiang 1 Ewing, Richard Edward 1 Glowinski, Roland 1 Gottlieb, James J. 1 Hoppe, Ronald H. W. 1 Hou, Suchung 1 Hu, Hongling 1 Hu, Qiya 1 Huang, Hongci 1 Jiang, Bin 1 Jiang, Longlong 1 Kako, Takashi 1 Kawarada, Hideo 1 Kitagawa, Takashi 1 Ma, Jingtang 1 Ma, Rui 1 Mori, Masatake 1 Natori, Makoto 1 Périaux, Jacques F. 1 Peter, Malte Andreas 1 Qi, Liqun 1 Qin, Lizhen 1 Rannacher, Rolf 1 Reichel, Lothar 1 Rogers, Colin 1 Sloan, Ian Hugh 1 Ushijima, Teruo 1 Wang, Weike 1 Widlund, Olof B. 1 Wu, Jingzhu 1 Xi, Zhenghui 1 Xie, Ziqing 1 Yang, Chung-Chun 1 Yang, Xueqin 1 Yu, Xijun 1 Zeng, Jinping
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#### Serials

 24 Journal of Computational Mathematics 16 Mathematica Numerica Sinica 9 Numerische Mathematik 9 Science in China. Series A 7 Journal of Computational and Applied Mathematics 6 Computer Methods in Applied Mechanics and Engineering 6 Mathematics of Computation 6 SIAM Journal on Numerical Analysis 6 Chinese Journal of Numerical Mathematics and Applications 5 Science China. Mathematics 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 East-West Journal of Numerical Mathematics 4 International Journal of Numerical Analysis and Modeling 2 International Journal for Numerical Methods in Engineering 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Chinese Annals of Mathematics. Series B 2 Computational Methods in Applied Mathematics 2 Contemporary Mathematics 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 Israel Journal of Technology 1 Acta Mathematica Sinica 1 Annales de l’Institut Fourier 1 The Annals of Probability 1 Hokkaido Mathematical Journal 1 Transactions of the American Mathematical Society 1 Acta Mathematicae Applicatae Sinica 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Probability Theory and Related Fields 1 Computational Mechanics 1 Journal of Scientific Computing 1 Japan Journal of Industrial and Applied Mathematics 1 Annals of Physics 1 SIAM Journal on Scientific Computing 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Journal of Hunan University. Natural Sciences 1 RIMS Kokyuroku 1 New Journal of Physics 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Quantum Information Processing 1 Bulletin of the American Mathematical Society 1 Lecture Notes in Numerical and Applied Analysis 1 Lecture Notes in Physics 1 GAKUTO International Series. Mathematical Sciences and Applications 1 Annals of Mathematical Statistics 1 International Journal for Numerical Methods in Biomedical Engineering
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#### Fields

 125 Numerical analysis (65-XX) 69 Mechanics of deformable solids (74-XX) 65 Partial differential equations (35-XX) 17 General and overarching topics; collections (00-XX) 10 Fluid mechanics (76-XX) 9 Probability theory and stochastic processes (60-XX) 4 Ordinary differential equations (34-XX) 4 Quantum theory (81-XX) 2 Potential theory (31-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

125 Publications have been cited 993 times in 484 Documents Cited by Year
A convergence condition for the quadrilateral Wilson element. Zbl 0581.65008
Shi, Zhongci
1984
On the error estimates of Morley element. Zbl 0850.73337
Shi, Zhongci
1990
Constrained quadrilateral nonconforming rotated $$\mathcal G_{1}$$ element. Zbl 1086.65111
Hu, Jun; Shi, Zhong-ci
2005
The F-E-M-test for convergence of nonconforming finite elements. Zbl 0648.65075
Shi, Zhong-ci
1987
A new class of Zienkiewicz-type non-conforming element in any dimensions. Zbl 1118.65124
Wang, Ming; Shi, Zhong-ci; Xu, Jinchao
2007
Some $$n$$-rectangle nonconforming elements for fourth order elliptic equations. Zbl 1142.65451
Wang, Ming; Shi, Zhongci; Xu, Jinchao
2007
A convergent nonconforming adaptive finite element method with quasi-optimal complexity. Zbl 1208.65154
Becker, Roland; Mao, Shipeng; Shi, Zhongci
2010
Lower order rectangular nonconforming mixed finite elements for plane elasticity. Zbl 1166.65395
Hu, Jun; Shi, Zhong-Ci
2008
A new superconvergence property of Wilson nonconforming finite element. Zbl 0897.65063
Shi, Zhongci; Jiang, Bin; Xue, Weimin
1997
A new a posteriori error estimate for the Morley element. Zbl 1169.74646
Hu, Jun; Shi, Zhongci
2009
Nonconforming rotated $$\mathcal Q_ 1$$ element for Reissner-Mindlin plate. Zbl 1037.74048
Ming, Pingbing; Shi, Zhongci
2001
On the convergence of the incomplete biquadratic nonconforming plate element. Zbl 0587.73114
Shi, Zhongci
1986
Lower-order rectangular nonconforming mixed finite element for the three-dimensional elasticity problem. Zbl 1156.74045
Man, Hongying; Hu, Jun; Shi, Zhongci
2009
Convergence and optimality of the adaptive Morley element method. Zbl 1255.65212
Hu, Jun; Shi, Zhongci; Xu, Jinchao
2012
A multilevel successive iteration method for nonlinear elliptic problems. Zbl 1042.65101
Huang, Yunqing; Shi, Zhongci; Tang, Tao; Xue, Weimin
2004
On the error bounds of nonconforming finite elements. Zbl 1211.65148
Mao, Shipeng; Shi, Zhongci
2010
Convergence of a standard adaptive nonconforming finite element method with optimal complexity. Zbl 1202.65147
Mao, Shipeng; Zhao, Xuying; Shi, Zhongci
2010
Economical cascadic multigrid method (ECMG). Zbl 1153.65046
Shi, Zhong-ci; Xu, Xue-jun; Huang, Yun-qing
2007
A remark on the optimal order of convergence of Wilson’s nonconforming element. Zbl 0607.65071
Shi, Zhongci
1986
The generalized patch test for Zienkiewicz triangles. Zbl 0564.73069
Shi, Zhong-ci
1984
Cascadic multigrid for parabolic problems. Zbl 0964.65103
Shi, Zhongci; Xu, Xuejun
2000
The best $$L^2$$ norm error estimate of lower order finite element methods for the fourth order problem. Zbl 1274.65292
Hu, Jun; Shi, Zhongci
2012
Coterminal families and the strong Markov property. Zbl 0275.60084
Pittenger, A. O.; Shih, C. T.
1973
On spline finite element method. Zbl 0452.73062
Shih, Chung-tze
1979
Convergence of the TRUNC plate element. Zbl 0616.73069
Shi, Zhongci
1987
High-accuracy analysis of two nonconforming plate elements. Zbl 1155.74045
Mao, Shipeng; Shi, Zhongci
2009
Double set parameter method of constructing stiffness matrices. Zbl 0850.73278
Chen, Shaochun; Shi, Zhongci
1991
Cascadic multigrid method for elliptic problems. Zbl 0943.65143
Shi, Z.-C.; Xu, X.
1999
A new cascadic multigrid. Zbl 1004.65135
Shi, Zhongci; Xu, Xuejun
2001
A new a priori error estimate of nonconforming finite element methods. Zbl 1309.65125
Hu, Jun; Ma, Rui; Shi, Zhongci
2014
On an extrapolation cascade multigrid method. Zbl 1265.65194
Chen, Chuanmiao; Shi, Zhongci; Hu, Hongling
2011
An explicit analysis of Stummel’s patch test examples. Zbl 0557.65060
Shi, Zhongci
1984
Quadrilateral mesh. Zbl 1005.65131
Ming, Pingbing; Shi, Zhongci
2002
Superconvergence studies of quadrilateral nonconforming rotated $$Q_1$$ elements. Zbl 1096.65109
Ming, Pingbing; Shi, Zhong-Ci; Xu, Yun
2006
On the accuracy of the quasi-conforming and generalized conforming finite elements. Zbl 0736.73065
Shi, Zhongci
1990
Two nonconforming quadrilateral elements for the Reissner-Mindlin plate. Zbl 1096.74050
Ming, Pingbing; Shi, Zhongci
2005
Cascadic multigrid for finite volume methods for elliptic problems. Zbl 1069.65137
Shi, Zhongci; Xu, Xuejun; Man, Hongying
2004
Mathematical theory of some non-standard finite element methods. Zbl 0811.65093
Shi, Zhongci; Wang, Ming
1994
Convergence analysis of Bergan’s energy-orthogonal plate element. Zbl 0814.73066
Shi, Zhongci; Chen, Shaochun; Zhang, Fei
1994
Plate elements with high accuracy. Zbl 1010.74594
Shi, Zhong-Ci; Chen, Shao-Chun; Huang, Hong-Ci
1997
Two lower-order nonconforming rectangular elements for the Reissner-Mindlin plate. Zbl 1118.74050
Hu, Jun; Shi, Zhongci
2007
A lower bound of the $$L^2$$ norm error estimate for the Adini element of the biharmonic equation. Zbl 1402.65160
Hu, Jun; Shi, Zhongci
2013
Quadrilateral mesh revisited. Zbl 1035.65147
Ming, Pingbing; Shi, Zhong Ci
2002
Nonconforming quadrilateral rotated $$Q_1$$ element for Reissner-Mindlin plate. Zbl 1038.74044
Hu, Jun; Ming, Pingbing; Shi, Zhongci
2003
Efficient solvers for saddle-point problems arising from domain decompositions with Lagrange multipliers. Zbl 1083.65112
Hu, Qiya; Shi, Zhongci; Yu, Dehao
2004
Vibration analysis of Kirchhoff plates by the Morley element method. Zbl 1129.74046
Huang, Jianguo; Guo, Ling; Shi, Zhongci
2008
Analysis for quadrilateral MITC elements for the Reissner-Mindlin plate problem. Zbl 1223.74027
Hu, Jun; Shi, Zhong-Ci
2009
Explicit error estimates for mixed and nonconforming finite elements. Zbl 1212.65424
Mao, Shipeng; Shi, Zhongci
2009
On the convergence properties of the quadrilateral elements of Sander and Beckers. Zbl 0557.65072
Shi, Zhongci
1984
Cascadic multigrid method for the second order elliptic problem. Zbl 0919.65072
Shi, Z.-C.; Xu, X.
1998
Adaptive finite element methods on quadrilateral meshes without hanging nodes. Zbl 1216.65165
Zhao, Xuying; Mao, Shipeng; Shi, Zhongci
2010
On extending potential theory to all strong Markov processes. Zbl 0193.46201
Shih, C. T.
1970
Analysis of some low-order quadrilateral Reissner-Mindlin plate elements. Zbl 1088.74045
Ming, Pingbing; Shi, Zhongci
2006
Some studies on mathematical models for general elastic multi-structures. Zbl 1093.74044
Huang, Jianguo; Shi, Zhongci; Xu, Yifeng
2005
A convergent adaptive finite element method with optimal complexity. Zbl 1171.65073
Becker, Roland; Mao, Shipeng; Shi, Zhong-Ci
2008
Convergence properties of two nonconforming finite elements. Zbl 0543.65073
Shi, Zhongci
1985
On the convergence rate of the boundary penalty method. Zbl 0547.65071
Shi, Zhong-Ci
1984
A multigrid method for Bergan’s energy-orthogonal plate element. Zbl 0835.73083
Shi, Zhongci; Yu, Xijun; Xie, Zhenghui
1995
Convergence of a nine parameter generalized conforming element. Zbl 0850.73277
Shi, Zhongci; Chen, Shaochun
1991
Convergence analysis for quadrilateral rotated $$Q_1$$ elements. Zbl 1019.65082
Ming, Pingbing; Shi, Zhongci
2001
$$P_1$$-nonconforming quadrilateral finite volume element method and its cascadic multigrid algorithm for elliptic problems. Zbl 1102.65116
Man, Hongying; Shi, Zhongci
2006
Finite element analysis for general elastic multi-structures. Zbl 1102.74041
Huang, Jianguo; Shi, Zhongci; Xu, Yifeng
2006
Error estimates of triangular finite elements under a weak angle condition. Zbl 1168.65063
Mao, Shipeng; Shi, Zhongci
2009
Error analysis of quadrilateral Wilson element for Reissner-Mindlin plate. Zbl 1169.74609
Hu, Jun; Shi, Zhong-Ci
2008
Cascadic multigrid method for a plate bending problem. Zbl 0916.73062
Shi, Zhongci; Xu, Xuejun
1998
Mathematical theory of elastic structures. Zbl 0599.73052
Feng, Kang; Shi, Zhong Ci
1981
Construction of Markov processes from hitting distributions. Zbl 0204.50704
Shih, C. T.
1971
Nonconforming finite element methods. Zbl 1013.65121
Shi, Zhongci
2002
Optimal $$\mathcal{L}^2$$ error bounds for MITC3 type element. Zbl 1003.65123
Ming, Pingbing; Shi, Zhong-ci
2002
An efficient rectangular plate element. Zbl 1008.74078
Shi, Zhongci; Chen, Qianyong
2001
Vibration analysis for elastic multi-beam structures by the $$C^0$$-continuous time-stepping finite element method. Zbl 1310.74045
Lai, Junjiang; Huang, Jianguo; Shi, Zhongci
2010
On the interpolation error estimates for $$Q_1$$ quadrilateral finite elements. Zbl 1187.65123
Mao, Shipeng; Nicaise, Serge; Shi, Zhong-Ci
2009
A lumped mass finite element method for vibration analysis of elastic plate-plate structures. Zbl 1214.74014
Lai, Junjiang; Huang, Jianguo; Shi, Zhongci
2010
Adaptive quadrilateral and hexahedral finite element methods with hanging nodes and convergence analysis. Zbl 1240.65337
Zhao, Xuying; Mao, Shipeng; Shi, Zhongci
2010
A direct analysis of the 9-parameter quasi-conforming plate element. Zbl 0850.73334
Shi, Zhongci; Chen, Shaochun
1990
On the free formation of constructing stiffness matrices. Zbl 0850.73279
Chen, Shaochun; Shi, Zhongci
1991
A V-cycle multigrid method for TRUNC plate element. Zbl 0963.74065
Shi, Zhongci; Xu, Xuejun
2000
Mathematical analysis for quadrilateral rotated $$\mathcal Q_1$$ element. III: The effect of numerical integration. Zbl 1042.65095
Ming, Pingbing; Shi, Zhongci
2003
A note on the quadrilateral mesh condition $$RDP(N,\psi)$$. Zbl 1142.65430
Shi, Dongyang; Shi, Zhongci; Wu, Jingzhu
2007
On the convergence rate of a parallel nonoverlapping domain decomposition method. Zbl 1173.35041
Qin, LiZhen; Shi, ZhongCi; Xu, XueJun
2008
Coterminal families and the strong Markov property. Zbl 0239.60070
Pittenger, A. O.; Shih, C. T.
1972
Two lower order nonconforming quadrilateral elements for the Reissner-Mindlin plate. Zbl 1218.74016
Hu, Jun; Shi, Zhongci
2008
Error estimates of Morley triangular element satisfying the maximal angle condition. Zbl 1407.74089
Mao, Shipeng; Nicaise, Serge; Shi, Zhong-Ci
2010
An analysis of a nine parameter plate element of Specht. Zbl 0724.73240
Shi, Zhongci; Chen, Shaochun
1989
A unified formation of shape functions for two kinds of nonconforming plate bending elements. Zbl 0622.73086
Shi, Zhongci
1986
A V-cycle multigrid for quadrilateral rotated $$Q_1$$ element with numerical integration. Zbl 1036.65110
Shi, Zhongci; Xu, Xuejun
2003
$$V$$-cycle multigrid methods for Wilson nonconforming element. Zbl 0969.65110
Shi, Zhongci; Xu, Xuejun
2000
Dual combined finite element methods for non-Newtonian flow. II: Parameter-dependent problem. Zbl 1072.76567
Ming, Pingbing; Shi, Zhong-Ci
2000
On the 9-parameter quasi-conforming plate element. Zbl 0705.73240
Shi, Zhongci
1988
Nonconforming rotated $$Q_1$$ element on non-tensor product anisotropic meshes. Zbl 1112.65121
Mao, Shipeng; Shi, Zhongci
2006
Shear locking in a plane elasticity problem and the enhanced assumed strain method. Zbl 1252.74004
Braess, Dietrich; Ming, Pingbing; Shi, Zhong-Ci
2010
Two robust nonconforming $$H^2$$-elements for linear strain gradient elasticity. Zbl 1457.65206
Li, Hongliang; Ming, Pingbing; Shi, Zhong-ci
2017
On the convergence of nonconforming finite elements. Zbl 0659.65102
Shi, Zhongci
1985
Construction of right processes from hitting distributions. Zbl 0557.60056
Shih, C. T.
1984
Multigrid method for Wilson nonconforming finite element with numerical integration. Zbl 0930.65133
Shi, Zhong-Ci; Jiang, Bin
1998
Multigrid methods for Wilson nonconforming finite element with numerical integration. Zbl 0928.65151
Shi, Zhongci; Jiang, Bin
1997
Multigrid for the mortar-type nonconforming element method for nonsymmetric and indefinite problems. Zbl 1026.65101
Shi, Zhong-Ci; Xu, Xuejun; Chen, Jinru
2002
Multigrid for the Wilson mortar element method. Zbl 0982.65121
Shi, Zhongci; Xu, Xuejun
2001
On Stummel’s examples to the patch test. Zbl 0695.65060
Shi, Z.-C.
1989
Construction of Markov processes from hitting distributions. Zbl 0195.47703
Shih, C. T.
1971
The quadratic Specht triangle. Zbl 1463.65375
Li, Hongliang; Ming, Pingbing; Shi, Zhongci
2020
Two robust nonconforming $$H^2$$-elements for linear strain gradient elasticity. Zbl 1457.65206
Li, Hongliang; Ming, Pingbing; Shi, Zhong-ci
2017
Constrained nonconforming rotated $$Q_1$$ element methods of the Reissner-Mindlin plate problem. Zbl 1389.74028
Hu, Jun; Shi, Zhongci
2016
Superconvergence of three dimensional Morley elements on cuboid meshes for biharmonic equations. Zbl 1356.65233
Hu, Jun; Shi, Zhongci; Yang, Xueqin
2016
A new a priori error estimate of nonconforming finite element methods. Zbl 1309.65125
Hu, Jun; Ma, Rui; Shi, Zhongci
2014
Constraint-free adaptive FEMs on quadrilateral nonconforming meshes. Zbl 1310.65150
Zhao, Xuying; Shi, Zhong-Ci; Du, Qiang
2014
A lower bound of the $$L^2$$ norm error estimate for the Adini element of the biharmonic equation. Zbl 1402.65160
Hu, Jun; Shi, Zhongci
2013
Convergence and optimality of the adaptive Morley element method. Zbl 1255.65212
Hu, Jun; Shi, Zhongci; Xu, Jinchao
2012
The best $$L^2$$ norm error estimate of lower order finite element methods for the fourth order problem. Zbl 1274.65292
Hu, Jun; Shi, Zhongci
2012
On an extrapolation cascade multigrid method. Zbl 1265.65194
Chen, Chuanmiao; Shi, Zhongci; Hu, Hongling
2011
A convergent nonconforming adaptive finite element method with quasi-optimal complexity. Zbl 1208.65154
Becker, Roland; Mao, Shipeng; Shi, Zhongci
2010
On the error bounds of nonconforming finite elements. Zbl 1211.65148
Mao, Shipeng; Shi, Zhongci
2010
Convergence of a standard adaptive nonconforming finite element method with optimal complexity. Zbl 1202.65147
Mao, Shipeng; Zhao, Xuying; Shi, Zhongci
2010
Adaptive finite element methods on quadrilateral meshes without hanging nodes. Zbl 1216.65165
Zhao, Xuying; Mao, Shipeng; Shi, Zhongci
2010
Vibration analysis for elastic multi-beam structures by the $$C^0$$-continuous time-stepping finite element method. Zbl 1310.74045
Lai, Junjiang; Huang, Jianguo; Shi, Zhongci
2010
A lumped mass finite element method for vibration analysis of elastic plate-plate structures. Zbl 1214.74014
Lai, Junjiang; Huang, Jianguo; Shi, Zhongci
2010
Adaptive quadrilateral and hexahedral finite element methods with hanging nodes and convergence analysis. Zbl 1240.65337
Zhao, Xuying; Mao, Shipeng; Shi, Zhongci
2010
Error estimates of Morley triangular element satisfying the maximal angle condition. Zbl 1407.74089
Mao, Shipeng; Nicaise, Serge; Shi, Zhong-Ci
2010
Shear locking in a plane elasticity problem and the enhanced assumed strain method. Zbl 1252.74004
Braess, Dietrich; Ming, Pingbing; Shi, Zhong-Ci
2010
Convergence analysis of the adaptive finite element method with the red-green refinement. Zbl 1189.65276
Zhao, Xuying; Hu, Jun; Shi, Zhongci
2010
A new a posteriori error estimate for the Morley element. Zbl 1169.74646
Hu, Jun; Shi, Zhongci
2009
Lower-order rectangular nonconforming mixed finite element for the three-dimensional elasticity problem. Zbl 1156.74045
Man, Hongying; Hu, Jun; Shi, Zhongci
2009
High-accuracy analysis of two nonconforming plate elements. Zbl 1155.74045
Mao, Shipeng; Shi, Zhongci
2009
Analysis for quadrilateral MITC elements for the Reissner-Mindlin plate problem. Zbl 1223.74027
Hu, Jun; Shi, Zhong-Ci
2009
Explicit error estimates for mixed and nonconforming finite elements. Zbl 1212.65424
Mao, Shipeng; Shi, Zhongci
2009
Error estimates of triangular finite elements under a weak angle condition. Zbl 1168.65063
Mao, Shipeng; Shi, Zhongci
2009
On the interpolation error estimates for $$Q_1$$ quadrilateral finite elements. Zbl 1187.65123
Mao, Shipeng; Nicaise, Serge; Shi, Zhong-Ci
2009
Analysis of nonconforming rotated $$\mathcal{Q}_i$$ element for the Reissner-Mindlin plate problem. Zbl 1423.74545
Hu, Jun; Shi, Zhongci
2009
Lower order rectangular nonconforming mixed finite elements for plane elasticity. Zbl 1166.65395
Hu, Jun; Shi, Zhong-Ci
2008
Vibration analysis of Kirchhoff plates by the Morley element method. Zbl 1129.74046
Huang, Jianguo; Guo, Ling; Shi, Zhongci
2008
A convergent adaptive finite element method with optimal complexity. Zbl 1171.65073
Becker, Roland; Mao, Shipeng; Shi, Zhong-Ci
2008
Error analysis of quadrilateral Wilson element for Reissner-Mindlin plate. Zbl 1169.74609
Hu, Jun; Shi, Zhong-Ci
2008
On the convergence rate of a parallel nonoverlapping domain decomposition method. Zbl 1173.35041
Qin, LiZhen; Shi, ZhongCi; Xu, XueJun
2008
Two lower order nonconforming quadrilateral elements for the Reissner-Mindlin plate. Zbl 1218.74016
Hu, Jun; Shi, Zhongci
2008
The patch recovery for finite element approximation of elasticity problems under quadrilateral meshes. Zbl 1141.74042
Shi, Zhongci; Xu, Xuejun; Zhang, Zhimin
2008
A new class of Zienkiewicz-type non-conforming element in any dimensions. Zbl 1118.65124
Wang, Ming; Shi, Zhong-ci; Xu, Jinchao
2007
Some $$n$$-rectangle nonconforming elements for fourth order elliptic equations. Zbl 1142.65451
Wang, Ming; Shi, Zhongci; Xu, Jinchao
2007
Economical cascadic multigrid method (ECMG). Zbl 1153.65046
Shi, Zhong-ci; Xu, Xue-jun; Huang, Yun-qing
2007
Two lower-order nonconforming rectangular elements for the Reissner-Mindlin plate. Zbl 1118.74050
Hu, Jun; Shi, Zhongci
2007
A note on the quadrilateral mesh condition $$RDP(N,\psi)$$. Zbl 1142.65430
Shi, Dongyang; Shi, Zhongci; Wu, Jingzhu
2007
A finite element method for investigating general elastic multi-structures. Zbl 1121.74057
Huang, Jianguo; Guo, Ling; Shi, Zhongci
2007
A new superconvergence property of nonconforming rotated $$Q_1$$ element in 3D. Zbl 1185.65202
Ming, Pingbing; Shi, Zhong-Ci; Xu, Yun
2007
Superconvergence studies of quadrilateral nonconforming rotated $$Q_1$$ elements. Zbl 1096.65109
Ming, Pingbing; Shi, Zhong-Ci; Xu, Yun
2006
Analysis of some low-order quadrilateral Reissner-Mindlin plate elements. Zbl 1088.74045
Ming, Pingbing; Shi, Zhongci
2006
$$P_1$$-nonconforming quadrilateral finite volume element method and its cascadic multigrid algorithm for elliptic problems. Zbl 1102.65116
Man, Hongying; Shi, Zhongci
2006
Finite element analysis for general elastic multi-structures. Zbl 1102.74041
Huang, Jianguo; Shi, Zhongci; Xu, Yifeng
2006
Nonconforming rotated $$Q_1$$ element on non-tensor product anisotropic meshes. Zbl 1112.65121
Mao, Shipeng; Shi, Zhongci
2006
Constrained quadrilateral nonconforming rotated $$\mathcal G_{1}$$ element. Zbl 1086.65111
Hu, Jun; Shi, Zhong-ci
2005
Two nonconforming quadrilateral elements for the Reissner-Mindlin plate. Zbl 1096.74050
Ming, Pingbing; Shi, Zhongci
2005
Some studies on mathematical models for general elastic multi-structures. Zbl 1093.74044
Huang, Jianguo; Shi, Zhongci; Xu, Yifeng
2005
The mortar element method for a nonlinear biharmonic equation. Zbl 1095.65105
Shi, Zhongci; Xu, Xuejun
2005
A multilevel successive iteration method for nonlinear elliptic problems. Zbl 1042.65101
Huang, Yunqing; Shi, Zhongci; Tang, Tao; Xue, Weimin
2004
Cascadic multigrid for finite volume methods for elliptic problems. Zbl 1069.65137
Shi, Zhongci; Xu, Xuejun; Man, Hongying
2004
Efficient solvers for saddle-point problems arising from domain decompositions with Lagrange multipliers. Zbl 1083.65112
Hu, Qiya; Shi, Zhongci; Yu, Dehao
2004
On the convergence of Weissman-Taylor element for Reissner-Mindlin plate. Zbl 1221.74072
Hu, Jun; Shi, Zhong-Ci
2004
Nonconforming quadrilateral rotated $$Q_1$$ element for Reissner-Mindlin plate. Zbl 1038.74044
Hu, Jun; Ming, Pingbing; Shi, Zhongci
2003
Mathematical analysis for quadrilateral rotated $$\mathcal Q_1$$ element. III: The effect of numerical integration. Zbl 1042.65095
Ming, Pingbing; Shi, Zhongci
2003
A V-cycle multigrid for quadrilateral rotated $$Q_1$$ element with numerical integration. Zbl 1036.65110
Shi, Zhongci; Xu, Xuejun
2003
Mathematical analysis for quadrilateral rotated $$\mathcal Q_1$$ element. II: Poincaré inequality and trace inequality. Zbl 1042.65094
Ming, Pingbing; Shi, Zhongci
2003
Some low-order quadrilateral Reissner-Mindlin plate elements. Zbl 1175.74084
Ming, Pingbing; Shi, Zhongci
2003
Quadrilateral mesh. Zbl 1005.65131
Ming, Pingbing; Shi, Zhongci
2002
Quadrilateral mesh revisited. Zbl 1035.65147
Ming, Pingbing; Shi, Zhong Ci
2002
Nonconforming finite element methods. Zbl 1013.65121
Shi, Zhongci
2002
Optimal $$\mathcal{L}^2$$ error bounds for MITC3 type element. Zbl 1003.65123
Ming, Pingbing; Shi, Zhong-ci
2002
Multigrid for the mortar-type nonconforming element method for nonsymmetric and indefinite problems. Zbl 1026.65101
Shi, Zhong-Ci; Xu, Xuejun; Chen, Jinru
2002
Nonconforming rotated $$\mathcal Q_ 1$$ element for Reissner-Mindlin plate. Zbl 1037.74048
Ming, Pingbing; Shi, Zhongci
2001
A new cascadic multigrid. Zbl 1004.65135
Shi, Zhongci; Xu, Xuejun
2001
Convergence analysis for quadrilateral rotated $$Q_1$$ elements. Zbl 1019.65082
Ming, Pingbing; Shi, Zhongci
2001
An efficient rectangular plate element. Zbl 1008.74078
Shi, Zhongci; Chen, Qianyong
2001
Multigrid for the Wilson mortar element method. Zbl 0982.65121
Shi, Zhongci; Xu, Xuejun
2001
Cascadic multigrid for parabolic problems. Zbl 0964.65103
Shi, Zhongci; Xu, Xuejun
2000
A V-cycle multigrid method for TRUNC plate element. Zbl 0963.74065
Shi, Zhongci; Xu, Xuejun
2000
$$V$$-cycle multigrid methods for Wilson nonconforming element. Zbl 0969.65110
Shi, Zhongci; Xu, Xuejun
2000
Dual combined finite element methods for non-Newtonian flow. II: Parameter-dependent problem. Zbl 1072.76567
Ming, Pingbing; Shi, Zhong-Ci
2000
Stable conforming and nonconforming finite element methods for the non-Newtonian flow. Zbl 1072.76568
Ming, Pingbing; Shi, Zhong-Ci
2000
Convergence analysis of a class of nonconforming finite elements. Zbl 0949.65111
Shi, Zhongci; Wang, Jiacheng
2000
Numerical treatment of multiphase flows in porous media. Proceedings of the international workshop, Beijing, China, August 2–6, 1999. Zbl 0986.00070
Chen, Zhangxin; Ewing, Richard E.; Shi, Zhong-Ci
2000
Cascadic multigrid method for elliptic problems. Zbl 0943.65143
Shi, Z.-C.; Xu, X.
1999
Cascadic multigrid for elliptic problems. Zbl 0953.65091
Shi, Zhong-Ci; Xu, Xuejun
1999
Cascadic multigrid method for the second order elliptic problem. Zbl 0919.65072
Shi, Z.-C.; Xu, X.
1998
Cascadic multigrid method for a plate bending problem. Zbl 0916.73062
Shi, Zhongci; Xu, Xuejun
1998
Multigrid method for Wilson nonconforming finite element with numerical integration. Zbl 0930.65133
Shi, Zhong-Ci; Jiang, Bin
1998
Substructure preconditioners for nonconforming plate elements. Zbl 0928.74104
Shi, Zhongci; Xie, Zhenghui
1998
Intergrid transfer operators for biharmonic problems using nonconforming plate elements on non-nested meshes. Zbl 0940.74069
Shi, Zhongci; Xie, Zhenghui
1998
A new superconvergence property of Wilson nonconforming finite element. Zbl 0897.65063
Shi, Zhongci; Jiang, Bin; Xue, Weimin
1997
Plate elements with high accuracy. Zbl 1010.74594
Shi, Zhong-Ci; Chen, Shao-Chun; Huang, Hong-Ci
1997
Multigrid methods for Wilson nonconforming finite element with numerical integration. Zbl 0928.65151
Shi, Zhongci; Jiang, Bin
1997
Domain decomposition methods in sciences and engineering. Proceedings of the 8th international conference, Beijing, China, May 16–20, 1995. Zbl 1024.65001
Glowinski, R.; Périaux, J.; Shi, Z.-C.; Widlund, O.
1997
Mathematical theory of elastic structures. Rev. ed. of the orig. Chinese ed. 1981. Zbl 0871.73001
Feng, Kang; Shi, Zhong-Ci
1996
A multigrid method for Bergan’s energy-orthogonal plate element. Zbl 0835.73083
Shi, Zhongci; Yu, Xijun; Xie, Zhenghui
1995
Mathematical theory of some non-standard finite element methods. Zbl 0811.65093
Shi, Zhongci; Wang, Ming
1994
Convergence analysis of Bergan’s energy-orthogonal plate element. Zbl 0814.73066
Shi, Zhongci; Chen, Shaochun; Zhang, Fei
1994
Computational mathematics in China. Zbl 0793.00023
Shi, Zhong-Ci; Yang, Chung-Chun
1994
Construction of Markov processes from hitting distributions without quasi-left-continuity. Zbl 0771.60054
Shih, C. T.
1992
Double set parameter method of constructing stiffness matrices. Zbl 0850.73278
Chen, Shaochun; Shi, Zhongci
1991
Convergence of a nine parameter generalized conforming element. Zbl 0850.73277
Shi, Zhongci; Chen, Shaochun
1991
On the free formation of constructing stiffness matrices. Zbl 0850.73279
Chen, Shaochun; Shi, Zhongci
1991
On piecing together locally defined Markov processes. Zbl 0744.60089
Shih, C. T.
1991
On the error estimates of Morley element. Zbl 0850.73337
Shi, Zhongci
1990
On the accuracy of the quasi-conforming and generalized conforming finite elements. Zbl 0736.73065
Shi, Zhongci
1990
...and 25 more Documents
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#### Cited by 532 Authors

 46 Shi, Dongyang 42 Shi, Zhongci 33 Hu, Jun 19 Chen, Shaochun 16 Huang, Jianguo 15 Carstensen, Carsten 15 Mao, Shipeng 15 Xu, Xuejun 14 Xie, Xiaoping 14 Yang, Yidu 14 Zhang, Shangyou 13 Zhang, Shuo 11 Bi, Hai 11 Huang, Yunqing 11 Ming, Pingbing 11 Xu, Jinchao 9 Huang, Xuehai 8 Brenner, Susanne Cecelia 8 Luo, Zhongxuan 8 Meng, Zhaoliang 7 Hu, Hongling 7 Pan, Kejia 7 Zhao, Yanmin 6 Chen, Chuanmiao 6 Guan, Hongbo 6 Li, Minghao 6 Ma, Rui 6 Sheen, Dongwoo 6 Zhou, Tianxiao 5 Gallistl, Dietmar 5 Li, Mingxia 5 Nataraj, Neela 5 Neilan, Michael 5 Pei, Lifang 5 Tang, Qili 5 Wang, Lieheng 5 Zhao, Xuying 4 Cen, Song 4 Chen, Jinru 4 Chen, Yanping 4 Duan, Huoyuan 4 Feischl, Michael 4 Guan, Xiaofei 4 Guo, Ling 4 He, Dongdong 4 Lai, Junjiang 4 Li, Hao 4 Li, Likang 4 Li, Xiaolin 4 Shen, Quan 4 Song, Shicang 4 Wang, Fenling 4 Wang, Ming 4 Xu, Chao 4 Yang, Xueqin 4 Yu, Guozhu 4 Zhang, Zhimin 4 Zhao, Jikun 3 Achchab, Boujemaa 3 Awanou, Gerard Michel 3 Becker, Roland 3 Boffi, Daniele 3 Chen, Long 3 Cui, Jintao 3 Han, Jiayu 3 Hu, Qiya 3 Huang, Qiumei 3 Korotov, Sergey 3 Li, Chenliang 3 Li, Rui 3 Li, Youai 3 Li, Zhenzhen 3 Lin, Qun 3 Liu, Qian 3 Liu, Wei 3 Lu, Linzhang 3 Man, Hongying 3 Pani, Amiya Kumar 3 Praetorius, Dirk 3 Qiao, Zhonghua 3 Ren, Jincheng 3 Shi, Xiangyu 3 Shu, Shi 3 Stenberg, Rolf 3 Wu, Shuonan 3 Wu, Yongke 3 Xie, Pingli 3 Yang, Huaijun 3 Yang, Yongqin 3 Zhang, Bei 3 Zhang, Yu 3 Zhou, Xinchen 2 Acosta, Gabriel 2 Andreev, Andrey Borissov 2 Arnold, Douglas Norman 2 Bai, Yanhong 2 Bertrand, Fleurianne 2 Bi, Chunjia 2 Bösing, Paulo Rafael 2 Bouihat, Khalid ...and 432 more Authors
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#### Cited in 82 Serials

 37 Numerische Mathematik 35 Journal of Scientific Computing 34 Mathematics of Computation 28 Computer Methods in Applied Mechanics and Engineering 27 Computers & Mathematics with Applications 27 Journal of Computational and Applied Mathematics 25 Applied Mathematics and Computation 22 Science China. Mathematics 16 Applied Numerical Mathematics 13 Numerical Methods for Partial Differential Equations 13 Advances in Computational Mathematics 13 Advances in Applied Mathematics and Mechanics 12 Science in China. Series A 12 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Applied Mathematics and Mechanics. (English Edition) 9 Applied Mathematics Letters 8 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 7 SIAM Journal on Numerical Analysis 7 Acta Mathematicae Applicatae Sinica. English Series 6 Numerical Algorithms 6 Computational Methods in Applied Mathematics 5 Journal of Computational Physics 5 International Journal for Numerical Methods in Engineering 5 Mathematical Problems in Engineering 4 Journal of Mathematical Analysis and Applications 4 BIT 4 Applied Mathematical Modelling 4 SIAM Journal on Scientific Computing 4 Communications in Numerical Methods in Engineering 3 Computing 3 Computational and Applied Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 2 Mathematical Methods in the Applied Sciences 2 Calcolo 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Numerical Functional Analysis and Optimization 2 Computational Mechanics 2 Japan Journal of Industrial and Applied Mathematics 2 Journal of Elasticity 2 Engineering Analysis with Boundary Elements 2 Journal of Inequalities and Applications 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Engineering Computations 2 Journal of Systems Science and Complexity 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Applied Mathematics and Computing 2 Central European Journal of Mathematics 2 Communications on Applied Mathematics and Computation 2 Electronic Research Archive 1 Indian Journal of Pure & Applied Mathematics 1 Results in Mathematics 1 SIAM Journal on Control and Optimization 1 Chinese Annals of Mathematics. Series B 1 Journal of Integral Equations and Applications 1 Applications of Mathematics 1 International Journal of Computer Mathematics 1 Applied Mathematics. Series B (English Edition) 1 International Applied Mechanics 1 International Journal of Computational Fluid Dynamics 1 Abstract and Applied Analysis 1 Taiwanese Journal of Mathematics 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Communications in Nonlinear Science and Numerical Simulation 1 Russian Physics Journal 1 Mathematical Modelling and Analysis 1 Journal of Applied Mathematics 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Journal of Numerical Mathematics 1 International Journal of Computational Methods 1 Advances in Difference Equations 1 The Australian Journal of Mathematical Analysis and Applications 1 Science in China. Series G 1 Boundary Value Problems 1 Inverse Problems in Science and Engineering 1 GAMM-Mitteilungen 1 Science China. Technological Sciences 1 International Journal for Numerical Methods in Biomedical Engineering 1 S$$\vec{\text{e}}$$MA Journal 1 ISRN Applied Mathematics 1 ISRN Computational Mathematics 1 East Asian Journal on Applied Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition)
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#### Cited in 23 Fields

 431 Numerical analysis (65-XX) 194 Partial differential equations (35-XX) 156 Mechanics of deformable solids (74-XX) 43 Fluid mechanics (76-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 7 Potential theory (31-XX) 7 Approximations and expansions (41-XX) 5 Ordinary differential equations (34-XX) 3 Optics, electromagnetic theory (78-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 History and biography (01-XX) 2 Operator theory (47-XX) 2 Convex and discrete geometry (52-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Geometry (51-XX) 1 (73-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)

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