## Xu, Jinchao

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 Author ID: xu.jinchao Published as: Xu, Jinchao; Xu, J.; Xu, Jin-chao; Xu, Jin-Chao; Xu, Jingchao; Xu, JinChao more...less Homepage: http://www.math.psu.edu/xu/ External Links: MGP · Wikidata · dblp · GND
 Documents Indexed: 204 Publications since 1982 8 Contributions as Editor Co-Authors: 149 Co-Authors with 190 Joint Publications 5,547 Co-Co-Authors
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### Co-Authors

 19 single-authored 23 Zikatanov, Ludmil T. 16 Chen, Long 14 Hu, Xiaozhe 14 Shu, Shi 14 Zhang, Chensong 13 Sun, Pengtao 11 Bramble, James H. 10 Lee, Youngju 9 Hong, Qingguo 8 Wu, Shuonan 8 Zhou, Aihui 7 Bank, Randolph E. 7 Pasciak, Joseph E. 6 He, Juncai 6 Hu, Kaibo 6 Wu, Jinbiao 5 Huang, Yunqing 5 Wang, Ming 5 Wu, Shuhong 5 Zhong, Liuqiang 4 Hu, Jun 4 Siegel, Jonathan W. 4 Xue, Guangri 4 Yang, Kai 4 Zhang, Shuo 4 Zheng, Bin 4 Zhu, Yunrong 3 Bacuta, Constantin 3 Feng, Chunsheng 3 Holst, Michael J. 3 Li, Zheng 3 Liu, Chun 3 Mu, Mo 3 Nochetto, Ricardo Horacio 3 Shi, Zhongci 3 Wang, Chaoyang 3 Widlund, Olof B. 3 Wittum, Gabriel 3 Xiao, Yingxiong 3 Xie, Xiaoping 3 Zhang, Lixiang 2 Bousquet, Arthur 2 Cai, Mingchao 2 Chan, Tony Fan-Cheong 2 Gong, Shihua 2 He, Yinnian 2 Hiptmair, Ralf 2 Kim, Hwanho 2 Knyazev, Andrew V. 2 Kornhuber, Ralf 2 Lin, Qun 2 Ma, Limin 2 Ma, Yicong 2 Mehrmann, Volker 2 Metti, Maximilian S. 2 Ming, Wang 2 Tai, Xuecheng 2 Vassilevski, Panayot Spirov 2 Wang, Junping 2 Ying, Longan 2 Zhang, Lian 1 Ayuso de Dios, Blanca 1 Babuška, Ivo 1 Brezzi, Franco 1 Caflisch, Russel E. 1 Cai, Xiao-Chuan 1 Carsel, Robert 1 Chen, Luoping 1 Chen, Shuangshuang 1 Chen, Yuyan 1 Cheng, Hwai-Ping 1 Cheng, Jing-Ru C. 1 Cho, Durkbin 1 Cui, Tao 1 Dai, Xiaoying 1 Dong, Bin 1 Glowinski, Roland 1 Grasedyck, Lars 1 Hao, Wenrui 1 Heimsund, Bjørn-Ove 1 Heumann, Holger 1 Hoppe, Ronald H. W. 1 Hu, Qiya 1 Hu, Yucheng 1 Huang, Xuehai 1 Jia, Jiwei 1 Jia, Xiaodong 1 Jin, Jicheng 1 Keyes, David Elliot 1 Kim, Kyungjoo 1 Kolev, Tzanio V. 1 Kraus, Johannes K. 1 Laguna, Pablo 1 Li, Jian 1 Li, Kun 1 Li, Ming-Hsu 1 Li, Qiaoyun 1 Li, Yukun 1 Li, Yuwen 1 Lin, Guang ...and 49 more Co-Authors
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### Serials

 29 Mathematics of Computation 17 Numerische Mathematik 15 Journal of Computational Mathematics 14 SIAM Journal on Numerical Analysis 10 Journal of Computational Physics 7 Computer Methods in Applied Mechanics and Engineering 7 Journal of Scientific Computing 6 SIAM Journal on Scientific Computing 5 Numerical Linear Algebra with Applications 5 Science China. Mathematics 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Computing and Visualization in Science 3 Journal of Computational and Applied Mathematics 3 Advances in Computational Mathematics 3 Lecture Notes in Computational Science and Engineering 3 Communications in Computational Physics 3 Advances in Applied Mathematics and Mechanics 3 Research in the Mathematical Sciences 2 Computing 2 Mathematica Numerica Sinica 2 SIAM Review 2 Journal of Numerical Mathematics 2 Oberwolfach Reports 2 Numerical Mathematics: Theory, Methods and Applications 2 Scientia Sinica. Mathematica 1 Classical and Quantum Gravity 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 IEEE Transactions on Information Theory 1 IMA Journal of Numerical Analysis 1 BIT 1 International Journal for Numerical Methods in Engineering 1 Natural Science Journal of Xiangtan University 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of the American Mathematical Society 1 SIAM Journal on Matrix Analysis and Applications 1 Neural Networks 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 SIAM Journal on Applied Mathematics 1 Computational Optimization and Applications 1 Applied and Computational Harmonic Analysis 1 Methods and Applications of Analysis 1 Journal on Numerical Methods and Computer Applications 1 Journal of Applied Mechanics and Technical Physics 1 Computational Methods in Applied Mathematics 1 Multiscale Modeling & Simulation 1 Journal of Tongji University. Natural Science 1 Acta Numerica 1 International Journal of Numerical Analysis and Modeling 1 Contemporary Mathematics 1 Handbook of Numerical Analysis 1 Inverse Problems and Imaging
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### Fields

 191 Numerical analysis (65-XX) 103 Partial differential equations (35-XX) 44 Fluid mechanics (76-XX) 20 Mechanics of deformable solids (74-XX) 11 Optics, electromagnetic theory (78-XX) 10 Computer science (68-XX) 8 General and overarching topics; collections (00-XX) 5 Approximations and expansions (41-XX) 4 Ordinary differential equations (34-XX) 4 Functional analysis (46-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Geophysics (86-XX) 2 Operator theory (47-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

182 Publications have been cited 5,534 times in 3,044 Documents Cited by Year
Iterative methods by space decomposition and subspace correction. Zbl 0788.65037
Xu, Jinchao
1992
Two-grid discretization techniques for linear and nonlinear PDEs. Zbl 0860.65119
Xu, Jinchao
1996
A novel two-grid method for semilinear elliptic equations. Zbl 0795.65077
Xu, Jinchao
1994
A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow. Zbl 1146.76031
Mu, Mo; Xu, Jinchao
2007
Parallel multilevel preconditioners. Zbl 0703.65076
Bramble, James H.; Pasciak, Joseph E.; Xu, Jinchao
1990
A two-grid discretization scheme for eigenvalue problems. Zbl 0959.65119
Xu, Jinchao; Zhou, Aihui
2001
Local and parallel finite element algorithms based on two-grid discretizations. Zbl 0948.65122
Xu, Jinchao; Zhou, Aihui
2000
The method of alternating projections and the method of subspace corrections in Hilbert space. Zbl 0999.47015
Xu, Jinchao; Zikatanov, Ludmil
2002
Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. Zbl 1153.78006
Hiptmair, Ralf; Xu, Jinchao
2007
Numerical solution to a mixed Navier-Stokes/Darcy model by the two-grid approach. Zbl 1213.76131
Cai, Mingchao; Mu, Mo; Xu, Jinchao
2009
A monotone finite element scheme for convection-diffusion equations. Zbl 0931.65111
Xu, Jinchao; Zikatanov, Ludmil
1999
Some observations on Babuška and Brezzi theories. Zbl 1028.65115
Xu, Jinchao; Zikatanov, Ludmil
2003
Error estimates on a new nonlinear Galerkin method based on two-grid finite elements. Zbl 0853.65092
Marion, Martine; Xu, Jinchao
1995
Analysis of linear and quadratic simplicial finite volume methods for elliptic equations. Zbl 1169.65110
Xu, Jinchao; Zou, Qingsong
2009
Asymptotically exact a posteriori error estimators. I: Grids with superconvergence. Zbl 1058.65116
Bank, Randolph E.; Xu, Jinchao
2003
Convergence estimates for multigrid algorithms without regularity assumptions. Zbl 0727.65101
Bramble, James H.; Pasciak, Joseph E.; Wang, Junping; Xu, Jinchao
1991
Some nonoverlapping domain decomposition methods. Zbl 0913.65115
Xu, Jinchao; Zou, Jun
1998
Analysis of recovery type a posteriori error estimators for mildly structured grids. Zbl 1050.65103
Xu, Jinchao; Zhang, Zhimin
2004
Convergence and optimal complexity of adaptive finite element eigenvalue computations. Zbl 1159.65090
Dai, Xiaoying; Xu, Jinchao; Zhou, Aihui
2008
A new class of iterative methods for nonselfadjoint or indefinite problems. Zbl 0756.65050
Xu, Jinchao
1992
Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems. Zbl 0990.65128
Xu, Jinchao; Zhou, Aihui
2001
Some estimates for a weighted $$L^ 2$$ projection. Zbl 0722.65057
Bramble, James H.; Xu, Jinchao
1991
The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids. Zbl 0857.65129
Xu, J.
1996
Local and parallel finite element algorithms for the Stokes problem. Zbl 1145.65097
He, Yinnian; Xu, Jinchao; Zhou, Aihui; Li, Jian
2008
Convergence estimates for product iterative methods with applications to domain decomposition. Zbl 0754.65085
Bramble, James H.; Pasciak, Joseph E.; Wang, Junping; Xu, Jinchao
1991
Uniformly-stable finite element methods for Darcy-Stokes-Brinkman models. Zbl 1174.76013
Xie, Xiaoping; Xu, Jinchao; Xue, Guangri
2008
Local and parallel finite element algorithms for the Navier-Stokes problem. Zbl 1093.76035
He, Yinnian; Xu, Jinchao; Zhou, Aihui
2006
The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms. Zbl 0718.65081
Bramble, James H.; Pasciak, Joseph E.; Xu, Jinchao
1991
The Morley element for fourth order elliptic equations in any dimensions. Zbl 1092.65103
Ming, Wang; Xu, Jinchao
2006
Asymptotically exact a posteriori error estimators. II: General unstructured grids. Zbl 1058.65117
Bank, Randolph E.; Xu, Jinchao
2003
The finite element approximation of the nonlinear Poisson-Boltzmann equation. Zbl 1152.65478
Chen, Long; Holst, Michael J.; Xu, Jinchao
2007
Global and uniform convergence of subspace correction methods for some convex optimization problems. Zbl 0985.65065
Tai, Xue-Cheng; Xu, Jinchao
2002
Convergence and optimality of adaptive mixed finite element methods. Zbl 1198.65211
Chen, Long; Holst, Michael; Xu, Jinchao
2009
Local and parallel finite element algorithms for eigenvalue problems. Zbl 1015.65060
Xu, Jinchao; Zhou, Aihui
2002
Algebraic multigrid methods. Zbl 1378.65182
Xu, Jinchao; Zikatanov, Ludmil
2017
Preconditioning techniques for a mixed Stokes/Darcy model in porous medium applications. Zbl 1172.76023
Cai, Mingchao; Mu, Mo; Xu, Jinchao
2009
Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients. Zbl 1151.65097
Xu, Jinchao; Zhu, Yunrong
2008
Parallel multilevel preconditioners. Zbl 0725.65095
Bramble, J. H.; Pasciak, J. E.; Xu, J.
1990
Stable finite element methods preserving $$\nabla \cdot \boldsymbol{B}=0$$ exactly for MHD models. Zbl 1381.76174
Hu, Kaibo; Ma, Yicong; Xu, Jinchao
2017
Optimal anisotropic meshes for minimizing interpolation errors in $$L^p$$-norms. Zbl 1106.41013
Chen, Long; Sun, Pengtao; Xu, Jingchao
2007
Galerkin-wavelet methods for two-point boundary value problems. Zbl 0771.65050
Xu, Jin-Chao; Shann, Wei-Chang
1992
A new class of Zienkiewicz-type non-conforming element in any dimensions. Zbl 1118.65124
Wang, Ming; Shi, Zhong-ci; Xu, Jinchao
2007
Minimal finite element spaces for $$2m$$-th-order partial differential equations in $$\mathbb{R}^n$$. Zbl 1264.65199
Wang, Ming; Xu, Jinchao
2013
Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations. Zbl 1263.78012
Zhong, Liuqiang; Chen, Long; Shu, Shi; Wittum, Gabriel; Xu, Jinchao
2012
Robust preconditioners for incompressible MHD models. Zbl 1349.76629
Ma, Yicong; Hu, Kaibo; Hu, Xiaozhe; Xu, Jinchao
2016
Superconvergence of quadratic finite elements on mildly structured grids. Zbl 1195.65193
Huang, Yunqing; Xu, Jinchao
2008
Some $$n$$-rectangle nonconforming elements for fourth order elliptic equations. Zbl 1142.65451
Wang, Ming; Shi, Zhongci; Xu, Jinchao
2007
Lower bounds of the discretization error for piecewise polynomials. Zbl 1280.65118
Lin, Qun; Xie, Hehu; Xu, Jinchao
2014
A two-grid discretization method for decoupling systems of partial differential equations. Zbl 1119.65117
Jin, Jicheng; Shu, Shi; Xu, Jinchao
2006
Optimal Delaunay triangulations. Zbl 1048.65020
Chen, Long; Xu, Jinchao
2004
An algorithm for coarsening unstructured meshes. Zbl 0857.65034
Bank, Randolph E.; Xu, Jinchao
1996
An agglomeration multigrid method for unstructured grids. Zbl 0909.65102
Chan, Tony F.; Xu, Jinchao; Zikatanov, Ludmil
1998
Modified Morley element method for a fourth order elliptic singular perturbation problem. Zbl 1102.65118
Wang, Ming; Xu, Jin-chao; Hu, Yucheng
2006
On the stability and accuracy of partially and fully implicit schemes for phase field modeling. Zbl 1440.80003
Xu, Jinchao; Li, Yukun; Wu, Shuonan; Bousquet, Arthur
2019
Linear finite elements with high accuracy. Zbl 0577.65094
Lin, Qun; Xu, Jinchao
1985
Convergence and optimality of the adaptive Morley element method. Zbl 1255.65212
Hu, Jun; Shi, Zhongci; Xu, Jinchao
2012
A discontinuous Galerkin method for the fourth-order curl problem. Zbl 1289.76053
Hong, Qingguo; Hu, Jun; Shu, Shi; Xu, Jinchao
2012
New formulations, positivity preserving discretizations and stability analysis for non-Newtonian flow models. Zbl 1176.76068
Lee, Young-Ju; Xu, Jinchao
2006
The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems. Zbl 0699.65075
Bramble, James H.; Pasciak, Joseph E.; Xu, Jinchao
1988
A nonconforming finite element method for fourth order curl equations in $$\mathbb R^3$$. Zbl 1227.78024
Zheng, Bin; Hu, Qiya; Xu, Jinchao
2011
Optimal multilevel methods for $$H$$(grad), $$H$$(curl), and $$H$$(div) systems on graded and unstructured grids. Zbl 1193.65209
Xu, Jinchao; Chen, Long; Nochetto, Ricardo H.
2009
Optimal error estimates for Nédélec edge elements for time-harmonic Maxwell’s equations. Zbl 1212.65467
Zhong, Liuqiang; Shu, Shi; Wittum, Gabriel; Xu, Jinchao
2009
Energetically stable discretizations for charge transport and electrokinetic models. Zbl 1351.78040
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun
2016
Regularity estimates for elliptic boundary value problems in Besov spaces. Zbl 1031.65133
Bacuta, Constantin; Bramble, James H.; Xu, Jinchao
2003
On an energy minimizing basis for algebraic multigrid methods. Zbl 1077.65130
Xu, Jinchao; Zikatanov, Ludmil
2004
Robust subspace correction methods for nearly singular systems. Zbl 1151.65096
Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil
2007
Superconvergence of the gradient in piecewise linear finite-element approximation to a parabolic problem. Zbl 0678.65079
Thomée, Vidar; Xu, Jin-Chao; Zhang, Nai-Ying
1989
ReLU deep neural networks and linear finite elements. Zbl 1463.68072
He, Juncai; Li, Lin; Xu, Jinchao; Zheng, Chunyue
2020
Superconvergent derivative recovery for Lagrange triangular elements of degree $$p$$ on unstructured grids. Zbl 1156.65091
Bank, Randolph E.; Xu, Jinchao; Zheng, Bin
2007
Two-grid methods for time-harmonic Maxwell equations. Zbl 1289.78014
Zhong, Liuqiang; Shu, Shi; Wang, Junxian; Xu, J.
2013
A unified study of continuous and discontinuous Galerkin methods. Zbl 1412.65214
Hong, Qingguo; Wang, Fei; Wu, Shuonan; Xu, Jinchao
2019
Optimal multilevel methods for graded bisection grids. Zbl 1235.65144
Chen, Long; Nochetto, Ricardo H.; Xu, Jinchao
2012
A multigrid method based on graph matching for convection-diffusion equations. Zbl 1071.65167
Kim, HwanHo; Xu, Jinchao; Zikatanov, Ludmil
2003
An introduction to multilevel methods. Zbl 0903.65095
Xu, Jinchao
1997
A local post-processing technique for improving the accuracy in mixed finite-element approximations. Zbl 0688.65061
Bramble, James H.; Xu, Jinchao
1989
Nonconforming tetrahedral finite elements for fourth order elliptic equations. Zbl 1125.65105
Ming, Wang; Xu, Jinchao
2007
A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Zbl 1338.76054
Hong, Qingguo; Kraus, Johannes; Xu, Jinchao; Zikatanov, Ludmil
2016
A scalable consistent second-order SPH solver for unsteady low Reynolds number flows. Zbl 1423.76372
Trask, Nathaniel; Maxey, Martin; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Yang, Kai; Xu, Jinchao
2015
The method of subspace corrections. Zbl 0983.65133
Xu, Jinchao
2001
MgNet: a unified framework of multigrid and convolutional neural network. Zbl 1476.65026
He, Juncai; Xu, Jinchao
2019
A preconditioned GMRES method for nonsymmetric or indefinite problems. Zbl 0766.65034
Xu, Jinchao; Cai, Xiao-Chuan
1992
Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem. Zbl 1273.76274
Hu, Jun; Xu, Jinchao
2013
Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems. Zbl 1203.65261
Sun, Pengtao; Chen, Long; Xu, Jinchao
2010
Phase field model of thermo-induced Marangoni effects in the mixtures and its numerical simulations with mixed finite element method. Zbl 1364.76097
Sun, Pengtao; Liu, Chun; Xu, Jinchao
2009
A conforming finite element method for overlapping and nonmatching grids. Zbl 1019.65090
Huang, Yunqing; Xu, Jinchao
2003
High-order extended finite element methods for solving interface problems. Zbl 1442.74243
Xiao, Yuanming; Xu, Jinchao; Wang, Fei
2020
Regularity estimates for elliptic boundary value problems with smooth data on polygonal domains. Zbl 1050.65108
Bacuta, C.; Bramble, J. H.; Xu, J.
2003
A simple preconditioner for a discontinuous Galerkin method for the Stokes problem. Zbl 1299.76128
Ayuso De Dios, Blanca; Brezzi, Franco; Marini, L. Donatella; Xu, Jinchao; Zikatanov, Ludmil
2014
Stability and accuracy of adapted finite element methods for singularly perturbed problems. Zbl 1146.65059
Chen, Long; Xu, Jinchao
2008
Optimal solvers for fourth-order PDEs discretized on unstructured grids. Zbl 1293.65160
Zhang, Shuo; Xu, Jinchao
2014
A sharp convergence estimate for the method of subspace corrections for singular systems of equations. Zbl 1137.65058
Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil
2008
On the convergence of iterative methods for semidefinite linear systems. Zbl 1122.65033
Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil
2006
Approximation rates for neural networks with general activation functions. Zbl 1480.41007
Siegel, Jonathan W.; Xu, Jinchao
2020
A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem. Zbl 1123.76343
Sun, Pengtao; Russell, Robert D.; Xu, Jinchao
2007
Structure-preserving finite element methods for stationary MHD models. Zbl 1405.65151
Hu, Kaibo; Xu, Jinchao
2019
Well-posedness and robust preconditioners for discretized fluid-structure interaction systems. Zbl 1423.74936
Xu, Jinchao; Yang, Kai
2015
An introduction to multigrid convergence theory. Zbl 0938.65142
Xu, Jinchao
1997
Fast Poisson-based solvers for linear and nonlinear PDEs. Zbl 1228.65233
Xu, Jinchao
2011
Multiphase Allen-Cahn and Cahn-Hilliard models and their discretizations with the effect of pairwise surface tensions. Zbl 1380.65208
Wu, Shuonan; Xu, Jinchao
2017
Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor. Zbl 1457.65222
Wu, Shuonan; Gong, Shihua; Xu, Jinchao
2017
High-order approximation rates for shallow neural networks with cosine and $$\mathrm{ReLU}^k$$ activation functions. Zbl 07495639
Siegel, Jonathan W.; Xu, Jinchao
2022
An extended Galerkin analysis in finite element exterior calculus. Zbl 1492.65311
Hong, Qingguo; Li, Yuwen; Xu, Jinchao
2022
Optimal convergence rates for the orthogonal greedy algorithm. Zbl 1497.94027
Siegel, Jonathan W.; Xu, Jinchao
2022
Uniform stability and error analysis for some discontinuous Galerkin methods. Zbl 1474.65439
Hong, Qingguo; Xu, Jinchao
2021
An extended Galerkin analysis for elliptic problems. Zbl 1477.65219
Hong, Qingguo; Wu, Shuonan; Xu, Jinchao
2021
Helicity-conservative finite element discretization for incompressible MHD systems. Zbl 07513848
Hu, Kaibo; Lee, Young-Ju; Xu, Jinchao
2021
Multiscale and monolithic arbitrary Lagrangian-Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms. Zbl 07501590
Hao, Wenrui; Sun, Pengtao; Xu, Jinchao; Zhang, Lian
2021
ReLU deep neural networks and linear finite elements. Zbl 1463.68072
He, Juncai; Li, Lin; Xu, Jinchao; Zheng, Chunyue
2020
High-order extended finite element methods for solving interface problems. Zbl 1442.74243
Xiao, Yuanming; Xu, Jinchao; Wang, Fei
2020
Approximation rates for neural networks with general activation functions. Zbl 1480.41007
Siegel, Jonathan W.; Xu, Jinchao
2020
Finite neuron method and convergence analysis. Zbl 1473.65350
Xu, Jinchao
2020
A mixed discontinuous Galerkin method for linear elasticity with strongly imposed symmetry. Zbl 1435.65211
Wang, Fei; Wu, Shuonan; Xu, Jinchao
2020
Make $$\ell_1$$ regularization effective in training sparse CNN. Zbl 1480.90178
He, Juncai; Jia, Xiaodong; Xu, Jinchao; Zhang, Lian; Zhao, Liang
2020
On the stability and accuracy of partially and fully implicit schemes for phase field modeling. Zbl 1440.80003
Xu, Jinchao; Li, Yukun; Wu, Shuonan; Bousquet, Arthur
2019
A unified study of continuous and discontinuous Galerkin methods. Zbl 1412.65214
Hong, Qingguo; Wang, Fei; Wu, Shuonan; Xu, Jinchao
2019
MgNet: a unified framework of multigrid and convolutional neural network. Zbl 1476.65026
He, Juncai; Xu, Jinchao
2019
Structure-preserving finite element methods for stationary MHD models. Zbl 1405.65151
Hu, Kaibo; Xu, Jinchao
2019
New hybridized mixed methods for linear elasticity and optimal multilevel solvers. Zbl 1412.65211
Gong, Shihua; Wu, Shuonan; Xu, Jinchao
2019
Nonconforming finite element spaces for $$2m$$th order partial differential equations on $$\mathbb {R}^n$$ simplicial grids when $$m=n+1$$. Zbl 1407.65304
Wu, Shuonan; Xu, Jinchao
2019
Generalized Gaffney inequality and discrete compactness for discrete differential forms. Zbl 1428.65084
He, Juncai; Hu, Kaibo; Xu, Jinchao
2019
Newton solvers for drift-diffusion and electrokinetic equations. Zbl 1448.65151
Bousquet, Arthur; Hu, Xiaozhe; Metti, Maximilian S.; Xu, Jinchao
2018
Algebraic multigrid methods. Zbl 1378.65182
Xu, Jinchao; Zikatanov, Ludmil
2017
Stable finite element methods preserving $$\nabla \cdot \boldsymbol{B}=0$$ exactly for MHD models. Zbl 1381.76174
Hu, Kaibo; Ma, Yicong; Xu, Jinchao
2017
Multiphase Allen-Cahn and Cahn-Hilliard models and their discretizations with the effect of pairwise surface tensions. Zbl 1380.65208
Wu, Shuonan; Xu, Jinchao
2017
Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor. Zbl 1457.65222
Wu, Shuonan; Gong, Shihua; Xu, Jinchao
2017
An error-resilient redundant subspace correction method. Zbl 1364.65275
Cui, Tao; Xu, Jinchao; Zhang, Chen-Song
2017
Analytical decoupling techniques for fully implicit reservoir simulation. Zbl 1375.76187
Qiao, Changhe; Wu, Shuhong; Xu, Jinchao; Zhang, Chen-Song
2017
Numerical studies of a class of linear solvers for fine-scale petroleum reservoir simulation. Zbl 1364.76157
Li, Zheng; Wu, Shuhong; Zhang, Chen-Song; Xu, Jinchao; Feng, Chunsheng; Hu, Xiaozhe
2017
Robust preconditioners for incompressible MHD models. Zbl 1349.76629
Ma, Yicong; Hu, Kaibo; Hu, Xiaozhe; Xu, Jinchao
2016
Energetically stable discretizations for charge transport and electrokinetic models. Zbl 1351.78040
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun
2016
A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Zbl 1338.76054
Hong, Qingguo; Kraus, Johannes; Xu, Jinchao; Zikatanov, Ludmil
2016
A two-grid SA-AMG convergence bound that improves when increasing the polynomial degree. Zbl 1413.65062
Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao
2016
Modeling and simulations for fluid and rotating structure interactions. Zbl 1439.74119
Yang, Kai; Sun, Pengtao; Wang, Lu; Xu, Jinchao; Zhang, Lixiang
2016
A nearly optimal multigrid method for general unstructured grids. Zbl 1356.65241
Grasedyck, Lars; Wang, Lu; Xu, Jinchao
2016
Multilevel preconditioners for reaction-diffusion problems with discontinuous coefficients. Zbl 1353.65131
Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong
2016
Optimal finite element methods for interface problems. Zbl 1339.65224
Xu, Jinchao; Zhang, Shuo
2016
Fast multilevel solvers for a class of discrete fourth order parabolic problems. Zbl 1410.65386
Zheng, Bin; Chen, Luoping; Hu, Xiaozhe; Chen, Long; Nochetto, Ricardo H.; Xu, Jinchao
2016
A scalable consistent second-order SPH solver for unsteady low Reynolds number flows. Zbl 1423.76372
Trask, Nathaniel; Maxey, Martin; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Yang, Kai; Xu, Jinchao
2015
Well-posedness and robust preconditioners for discretized fluid-structure interaction systems. Zbl 1423.74936
Xu, Jinchao; Yang, Kai
2015
A multigrid solver based on distributive smoother and residual overweighting for Oseen problems. Zbl 1363.65155
Chen, Long; Hu, Xiaozhe; Wang, Ming; Xu, Jinchao
2015
A cascadic multigrid algorithm for computing the Fiedler vector of graph Laplacians. Zbl 1340.65262
Urschel, John C.; Xu, Jinchao; Hu, Xiaozhe; Zikatanov, Ludmil T.
2015
Lower bounds of the discretization error for piecewise polynomials. Zbl 1280.65118
Lin, Qun; Xie, Hehu; Xu, Jinchao
2014
A simple preconditioner for a discontinuous Galerkin method for the Stokes problem. Zbl 1299.76128
Ayuso De Dios, Blanca; Brezzi, Franco; Marini, L. Donatella; Xu, Jinchao; Zikatanov, Ludmil
2014
Optimal solvers for fourth-order PDEs discretized on unstructured grids. Zbl 1293.65160
Zhang, Shuo; Xu, Jinchao
2014
Full Eulerian finite element method of a phase field model for fluid-structure interaction problem. Zbl 1391.76359
Sun, Pengtao; Xu, Jinchao; Zhang, Lixiang
2014
Numerical study of geometric multigrid methods on CPU-GPU heterogeneous computers. Zbl 1305.78016
Feng, Chunsheng; Shu, Shi; Xu, Jinchao; Zhang, Chen-Song
2014
On adaptive Eulerian-Lagrangian method for linear convection-diffusion problems. Zbl 1335.65081
Hu, Xiaozhe; Lee, Young-Ju; Xu, Jinchao; Zhang, Chen-Song
2014
A multi-stage preconditioner for the black oil model and its OpenMP implementation. Zbl 1455.76179
Feng, Chunsheng; Shu, Shi; Xu, Jinchao; Zhang, Chen-Song
2014
Minimal finite element spaces for $$2m$$-th-order partial differential equations in $$\mathbb{R}^n$$. Zbl 1264.65199
Wang, Ming; Xu, Jinchao
2013
Two-grid methods for time-harmonic Maxwell equations. Zbl 1289.78014
Zhong, Liuqiang; Shu, Shi; Wang, Junxian; Xu, J.
2013
Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem. Zbl 1273.76274
Hu, Jun; Xu, Jinchao
2013
Application of auxiliary space preconditioning in field-scale reservoir simulation. Zbl 1305.86001
Hu, Xiaozhe; Xu, Jinchao; Zhang, Chensong
2013
Comparative convergence analysis of nonlinear AMLI-cycle multigrid. Zbl 1276.65089
Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao
2013
Combined preconditioning with applications in reservoir simulation. Zbl 1426.76269
Hu, Xiaozhe; Wu, Shuhong; Wu, Xiao-Hui; Xu, Jinchao; Zhang, Chen-Song; Zhang, Shiquan; Zikatanov, Ludmil
2013
A parallel auxiliary grid algebraic multigrid method for graphic processing units. Zbl 1275.65021
Wang, Lu; Hu, Xiaozhe; Cohen, Jonathan; Xu, Jinchao
2013
Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids. Zbl 1313.65324
Yu, Guozhu; Xu, Jinchao; Zikatanov, Ludmil T.
2013
Domain decomposition methods in science and engineering XX. Selected papers based on the presentations of the 20th international conference on domain decomposition, San Diego, CA, USA, February 9–13, 2011. Zbl 1416.65007
2013
Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations. Zbl 1263.78012
Zhong, Liuqiang; Chen, Long; Shu, Shi; Wittum, Gabriel; Xu, Jinchao
2012
Convergence and optimality of the adaptive Morley element method. Zbl 1255.65212
Hu, Jun; Shi, Zhongci; Xu, Jinchao
2012
A discontinuous Galerkin method for the fourth-order curl problem. Zbl 1289.76053
Hong, Qingguo; Hu, Jun; Shu, Shi; Xu, Jinchao
2012
Optimal multilevel methods for graded bisection grids. Zbl 1235.65144
Chen, Long; Nochetto, Ricardo H.; Xu, Jinchao
2012
Convergence analysis of $$V$$-cycle multigrid methods for anisotropic elliptic equations. Zbl 1258.65093
Wu, Yongke; Chen, Long; Xie, Xiaoping; Xu, Jinchao
2012
Fully discrete semi-Lagrangian methods for advection of differential forms. Zbl 1267.65130
Heumann, Holger; Hiptmair, Ralf; Li, Kun; Xu, Jinchao
2012
A nonconforming finite element method for fourth order curl equations in $$\mathbb R^3$$. Zbl 1227.78024
Zheng, Bin; Hu, Qiya; Xu, Jinchao
2011
Fast Poisson-based solvers for linear and nonlinear PDEs. Zbl 1228.65233
Xu, Jinchao
2011
New mixed finite elements for plane elasticity and Stokes equations. Zbl 1235.74324
Xie, XiaoPing; Xu, JinChao
2011
Handbook of numerical analysis. Vol XVI. Special Volume: Numerical methods for non-Newtonian fluids. Zbl 1216.76001
2011
Stable finite element discretizations for viscoelastic flow models. Zbl 1318.76010
Lee, Young-Ju; Xu, Jinchao; Zhang, Chen-Song
2011
A high order adaptive finite element method for solving nonlinear hyperbolic conservation laws. Zbl 1249.65207
Xu, Zhengfu; Xu, Jinchao; Shu, Chiwang
2011
Global existence, uniqueness and optimal solvers of discretized viscoelastic flow models. Zbl 1225.76198
Lee, Young-Ju; Xu, Jinchao; Zhang, Chen-Song
2011
Robust preconditioner for H(curl) interface problems. Zbl 1217.78062
Xu, Jinchao; Zhu, Yunrong
2011
Domain decomposition methods in science and engineering XIX. Selected papers based on the presentations at the 19th international conference on domain decoposition (DD19), Zhanjiajie, China, August 17–22, 2009. Zbl 1204.65002
2011
Effects of integrations and adaptivity for the Eulerian-Lagrangian method. Zbl 1249.65197
Jia, Jiwei; Hu, Xiaozhe; Xu, Jinchao; Zhang, Chensong
2011
Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems. Zbl 1203.65261
Sun, Pengtao; Chen, Long; Xu, Jinchao
2010
A generalization of the vertex-centered finite volume scheme to arbitrary high order. Zbl 1207.65128
Vogel, Andreas; Xu, Jinchao; Wittum, Gabriel
2010
Convergence of adaptive edge finite element methods for $${\mathbf H}({\mathbf curl})$$-elliptic problems. Zbl 1240.65338
Zhong, Liuqiang; Shu, Shi; Chen, Long; Xu, Jinchao
2010
Numerical solution to a mixed Navier-Stokes/Darcy model by the two-grid approach. Zbl 1213.76131
Cai, Mingchao; Mu, Mo; Xu, Jinchao
2009
Analysis of linear and quadratic simplicial finite volume methods for elliptic equations. Zbl 1169.65110
Xu, Jinchao; Zou, Qingsong
2009
Convergence and optimality of adaptive mixed finite element methods. Zbl 1198.65211
Chen, Long; Holst, Michael; Xu, Jinchao
2009
Preconditioning techniques for a mixed Stokes/Darcy model in porous medium applications. Zbl 1172.76023
Cai, Mingchao; Mu, Mo; Xu, Jinchao
2009
Optimal multilevel methods for $$H$$(grad), $$H$$(curl), and $$H$$(div) systems on graded and unstructured grids. Zbl 1193.65209
Xu, Jinchao; Chen, Long; Nochetto, Ricardo H.
2009
Optimal error estimates for Nédélec edge elements for time-harmonic Maxwell’s equations. Zbl 1212.65467
Zhong, Liuqiang; Shu, Shi; Wittum, Gabriel; Xu, Jinchao
2009
Phase field model of thermo-induced Marangoni effects in the mixtures and its numerical simulations with mixed finite element method. Zbl 1364.76097
Sun, Pengtao; Liu, Chun; Xu, Jinchao
2009
Fast numerical simulation of two-phase transport model in the cathode of a polymer electrolyte fuel cell. Zbl 1364.82058
Sun, Pengtao; Xue, Guangri; Wang, Chaoyang; Xu, Jinchao
2009
Auxiliary space preconditioners for mixed finite element methods. Zbl 1183.65151
Tuminaro, Ray S.; Xu, Jinchao; Zhu, Yunrong
2009
A domain decomposition method for two-phase transport model in the cathode of a polymer electrolyte fuel cell. Zbl 1280.76048
Sun, Pengtao; Xue, Guangri; Wang, Chao-Yang; Xu, Jinchao
2009
New numerical techniques for a three-dimensional liquid-feed direct methanol fuel cell model. Zbl 1191.82044
Sun, Pengtao; Xue, Guangri; Wang, Chaoyang; Xu, Jinchao
2009
Convergence and optimal complexity of adaptive finite element eigenvalue computations. Zbl 1159.65090
Dai, Xiaoying; Xu, Jinchao; Zhou, Aihui
2008
Local and parallel finite element algorithms for the Stokes problem. Zbl 1145.65097
He, Yinnian; Xu, Jinchao; Zhou, Aihui; Li, Jian
2008
Uniformly-stable finite element methods for Darcy-Stokes-Brinkman models. Zbl 1174.76013
Xie, Xiaoping; Xu, Jinchao; Xue, Guangri
2008
Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients. Zbl 1151.65097
Xu, Jinchao; Zhu, Yunrong
2008
Superconvergence of quadratic finite elements on mildly structured grids. Zbl 1195.65193
Huang, Yunqing; Xu, Jinchao
2008
Stability and accuracy of adapted finite element methods for singularly perturbed problems. Zbl 1146.65059
Chen, Long; Xu, Jinchao
2008
A sharp convergence estimate for the method of subspace corrections for singular systems of equations. Zbl 1137.65058
Lee, Young-Ju; Wu, Jinbiao; Xu, Jinchao; Zikatanov, Ludmil
2008
New estimates for the rate of convergence of the method of subspace corrections. Zbl 1174.65354
Cho, Durkbin; Xu, Jinchao; Zikatanov, Ludmil
2008
Convergence analysis of iterative methods for semidefinite systems. Zbl 1174.65013
Wu, Jinbiao; Lee, Youngju; Xu, Jinchao; Zikatanov, Ludmil
2008
Optimal algorithms for discretized partial differential equations. Zbl 1180.65156
Xu, Jinchao
2008
A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow. Zbl 1146.76031
Mu, Mo; Xu, Jinchao
2007
Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. Zbl 1153.78006
Hiptmair, Ralf; Xu, Jinchao
2007
The finite element approximation of the nonlinear Poisson-Boltzmann equation. Zbl 1152.65478
Chen, Long; Holst, Michael J.; Xu, Jinchao
2007
...and 82 more Documents
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### Cited by 3,117 Authors

 91 Xu, Jinchao 63 Huang, Yunqing 52 He, Yinnian 48 Zhang, Zhimin 46 Chen, Yanping 41 Yang, Yidu 39 Shang, Yueqiang 38 Hou, Yanren 35 Zikatanov, Ludmil T. 34 Chen, Long 34 Xie, Hehu 31 Shu, Shi 30 Hu, Xiaozhe 28 Brenner, Susanne Cecelia 28 Hu, Jun 28 Xu, Xuejun 26 Bi, Hai 26 Li, Jian 25 Vassilevski, Panayot Spirov 25 Zou, Qingsong 24 Sun, Pengtao 23 He, Xiaoming 22 Bacuta, Constantin 22 Feng, Xinlong 21 Li, Jichun 20 Bramble, James H. 20 Carstensen, Carsten 20 Chen, Jinru 20 Du, Guangzhi 20 Shi, Dongyang 20 Yang, Danping 20 Zheng, Haibiao 20 Zhou, Aihui 19 Chen, Chuanjun 19 Huang, Qiumei 19 Zhang, Shangyou 19 Zhang, Shuo 18 Chen, Zhangxin 18 Oswald, Peter 18 Zou, Jun 18 Zuo, Liyun 17 Han, Jiayu 17 Huang, Pengzhan 17 Pasciak, Joseph E. 16 Griebel, Michael 15 Harbrecht, Helmut 15 Lin, Qun 15 Rui, Hongxing 14 Bi, Chunjia 14 Hu, Qiya 14 Li, Yonghai 14 Mao, Shipeng 14 Shi, Zhongci 14 Yang, Wei 14 Zhang, Chensong 14 Zhong, Liuqiang 13 Antonietti, Paola Francesca 13 Hiptmair, Ralf 13 Huang, Xuehai 13 Kraus, Johannes K. 13 Lee, Youngju 13 Stevenson, Rob P. 13 Wang, Cheng 12 Huang, Jianguo 12 Neilan, Michael 12 Xie, Xiaoping 12 Yan, Ningning 11 Gatica, Gabriel N. 11 Gunzburger, Max D. 11 Guo, Hailong 11 Holst, Michael J. 11 Hong, Qingguo 11 Lazarov, Raytcho D. 11 Liu, Chun 11 Tai, Xuecheng 11 Wang, Yang 11 Wu, Shuonan 11 Yang, Xiaofeng 11 Zeng, Jinping 11 Zhao, Xin 10 An, Rong 10 Bank, Randolph E. 10 Chen, Shaochun 10 Dahmen, Wolfgang A. 10 Demlow, Alan 10 Führer, Thomas 10 Hu, Hanzhang 10 Křížek, Michal 10 Li, Hengguang 10 Li, Likang 10 Li, Yuwen 10 Lin, Yanping 10 Praetorius, Dirk 10 Sayas, Francisco-Javier 10 Shi, Feng 10 Wang, Junping 10 Wittum, Gabriel 10 Yserentant, Harry 10 Zhang, Jiansong 10 Zhang, Yu ...and 3,017 more Authors
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### Cited in 234 Serials

 202 Journal of Scientific Computing 189 Journal of Computational and Applied Mathematics 171 Computer Methods in Applied Mechanics and Engineering 165 Mathematics of Computation 164 Computers & Mathematics with Applications 157 Journal of Computational Physics 146 Numerische Mathematik 131 SIAM Journal on Scientific Computing 109 Applied Mathematics and Computation 102 Applied Numerical Mathematics 80 SIAM Journal on Numerical Analysis 79 Advances in Computational Mathematics 68 Numerical Methods for Partial Differential Equations 54 Numerical Linear Algebra with Applications 51 Numerical Algorithms 41 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 41 Communications in Computational Physics 37 Advances in Applied Mathematics and Mechanics 36 International Journal of Computer Mathematics 35 Science China. Mathematics 34 Computational Methods in Applied Mathematics 32 BIT 31 Computing 30 Calcolo 26 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 23 Journal of Mathematical Analysis and Applications 21 Applied Mathematics Letters 20 International Journal of Numerical Analysis and Modeling 18 Applications of Mathematics 17 Linear Algebra and its Applications 16 Computers and Fluids 16 Applied Mathematics and Mechanics. (English Edition) 16 Computational Geosciences 15 Mathematical Methods in the Applied Sciences 15 Abstract and Applied Analysis 15 Journal of Numerical Mathematics 14 Mathematical Problems in Engineering 14 Computing and Visualization in Science 14 Multiscale Modeling & Simulation 14 East Asian Journal on Applied Mathematics 13 International Journal for Numerical Methods in Engineering 13 Mathematics and Computers in Simulation 12 Applicable Analysis 12 RAIRO. Modélisation Mathématique et Analyse Numérique 12 Computational and Applied Mathematics 12 Discrete and Continuous Dynamical Systems. Series B 11 Numerical Functional Analysis and Optimization 10 Applied Mathematical Modelling 10 Engineering Analysis with Boundary Elements 9 Journal of Computational Mathematics 9 ETNA. Electronic Transactions on Numerical Analysis 8 Acta Mathematicae Applicatae Sinica. English Series 8 Constructive Approximation 8 Science in China. Series A 8 Journal of Applied Mathematics and Computing 8 Results in Applied Mathematics 7 Journal of Approximation Theory 7 SIAM Journal on Matrix Analysis and Applications 7 Communications in Numerical Methods in Engineering 7 Electronic Research Archive 6 Computational Mechanics 6 Foundations of Computational Mathematics 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Advances in Difference Equations 6 Communications on Applied Mathematics and Computation 5 International Journal for Numerical Methods in Fluids 5 Journal of Differential Equations 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 5 Mathematical Modelling and Analysis 5 International Journal of Computational Methods 5 Acta Numerica 5 Research in the Mathematical Sciences 5 SMAI Journal of Computational Mathematics 4 International Journal of Engineering Science 4 SIAM Journal on Control and Optimization 4 Computational Mathematics and Mathematical Physics 4 Applied Mathematics. Series B (English Edition) 4 Applied and Computational Harmonic Analysis 4 Journal of Systems Science and Complexity 4 Acta Mathematica Scientia. Series B. (English Edition) 4 Boundary Value Problems 4 Inverse Problems and Imaging 4 Molecular Based Mathematical Biology 4 AMM. Applied Mathematics and Mechanics. (English Edition) 3 Computer Physics Communications 3 Inverse Problems 3 Journal of Engineering Mathematics 3 Acta Applicandae Mathematicae 3 Computer Aided Geometric Design 3 COMPEL 3 Journal of Integral Equations and Applications 3 European Journal of Applied Mathematics 3 SIAM Review 3 Journal of Mathematical Imaging and Vision 3 Computational Optimization and Applications 3 International Journal of Computational Fluid Dynamics 3 Journal of Inequalities and Applications 3 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 3 Communications in Nonlinear Science and Numerical Simulation ...and 134 more Serials
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### Cited in 46 Fields

 2,740 Numerical analysis (65-XX) 1,391 Partial differential equations (35-XX) 781 Fluid mechanics (76-XX) 255 Mechanics of deformable solids (74-XX) 162 Optics, electromagnetic theory (78-XX) 120 Calculus of variations and optimal control; optimization (49-XX) 80 Computer science (68-XX) 55 Approximations and expansions (41-XX) 55 Biology and other natural sciences (92-XX) 40 Operations research, mathematical programming (90-XX) 39 Statistical mechanics, structure of matter (82-XX) 36 Linear and multilinear algebra; matrix theory (15-XX) 34 Operator theory (47-XX) 29 Probability theory and stochastic processes (60-XX) 28 Ordinary differential equations (34-XX) 24 Statistics (62-XX) 24 Geophysics (86-XX) 21 Integral equations (45-XX) 21 Classical thermodynamics, heat transfer (80-XX) 21 Information and communication theory, circuits (94-XX) 20 Real functions (26-XX) 19 Potential theory (31-XX) 19 Functional analysis (46-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 18 Global analysis, analysis on manifolds (58-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Quantum theory (81-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Combinatorics (05-XX) 8 Systems theory; control (93-XX) 5 Convex and discrete geometry (52-XX) 4 History and biography (01-XX) 4 Special functions (33-XX) 4 Mechanics of particles and systems (70-XX) 3 Differential geometry (53-XX) 3 Astronomy and astrophysics (85-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Functions of a complex variable (30-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geometry (51-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Relativity and gravitational theory (83-XX)

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