## Zhang, Shangyou

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 Author ID: zhang.shangyou Published as: Zhang, Shangyou; Zhang, ShangYou; Zhang, S. more...less
 Documents Indexed: 185 Publications since 1987 Co-Authors: 68 Co-Authors with 106 Joint Publications 1,976 Co-Co-Authors
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### Co-Authors

 20 single-authored 38 Ye, Xiu 13 Hu, Jun 8 Zhang, Zhimin 7 Barron, Ronald M. 7 Zhu, Peng 6 Mu, Lin 6 Wang, Junping 5 An, C-F. 5 Zhai, Qilong 4 Hsiao, George C. 4 Huang, Yunqing 4 Shaĭdurov, Vladimir Victorovich 4 Sorokina, Tatyana 4 Zhang, Ran 3 Duan, Huoyuan 3 Scott, Larkin Ridgway 3 Yang, Yin 3 Zhang, Tie 2 Cui, Ming 2 Feng, Yue 2 Gao, Fuzheng 2 Huang, Jianguo 2 Karunamuni, Rohana J. 2 Lapin, Aleksandr Vasil’evich 2 Li, Jichun 2 Lin, Qun 2 Lin, Runchang 2 Liu, Yujie 2 Man, Hongying 2 Mizukami, Koichi 2 Olagunju, David O. 2 Peng, Hui 2 Qin, Jinshui 2 Rudraiah, Nanjundappa 2 Shananin, Aleksandr Alekseevich 2 Tan, Roger C. E. 2 Wang, Chunmei 2 Wang, Jindi 2 Wang, Ruishu 2 Wang, Xiaoshen 2 Xu, Liwei 2 Xu, Xuejun 1 Ambainis, Andris 1 Bacuta, Constantin 1 Bagheri, Babak 1 Basser, Peter J. 1 Becker, Leigh C. 1 Bogy, David B. 1 Burton, Theodore Allen 1 Cai, Wei 1 Chen, Chuanmiao 1 Chen, Jinru 1 Chen, Wenbin 1 Childs, Andrew M. 1 Chiocca, E. Antonio 1 Dautov, Rafail Z. 1 Deisboeck, Thomas S. 1 Demiralp, Ç. 1 Deng, James Tian Quan 1 Domenech, Serge 1 Du, Zhijie 1 Duncan, James H. 1 Gao, Shaoqin 1 Gilbert, Robert Pertsch 1 Gogos, George 1 Greenberg, B. D. 1 Gutman, Ivan M. 1 Han, Houde 1 Han, Lei 1 Hu, Hongling 1 Huang, Xuehai 1 Huang, Zhongyi 1 Isakov, Victor M. 1 Jones, Michael Chris 1 Kabanikhin, Sergeĭ Igorevich 1 Karpov, Eduard G. 1 Keefe, Douglas H. 1 Ladas, Gerasimos E. 1 Laidlaw, David H. 1 Lapin, Serguei 1 Li, Mingxia 1 Liu, Wing Kam 1 Ma, Junhua 1 Mao, Shipeng 1 Marcozzi, Michael D. 1 Mi, X. B. 1 Monk, Peter B. 1 Mu, Mo 1 Muzio, Jon C. 1 Ni, Xiaowu 1 Pagaldipti, N. 1 Pierpaoli, C. 1 Qiao, Wanying 1 Qin, Lizhen 1 Rajadas, J. N. 1 Reichardt, Ben W. 1 Ruan, Shiling 1 Schinas, John 1 Shapiro, Vadim 1 Shishlenin, Maxim Aleksandrovich ...and 20 more Co-Authors
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### Serials

 17 Journal of Computational and Applied Mathematics 11 Mathematics of Computation 8 SIAM Journal on Numerical Analysis 7 Applied Numerical Mathematics 7 Journal of Scientific Computing 7 International Journal of Numerical Analysis and Modeling 6 Advances in Applied Mathematics and Mechanics 4 Computers & Mathematics with Applications 4 Computer Methods in Applied Mechanics and Engineering 4 Numerical Methods for Partial Differential Equations 4 Lobachevskii Journal of Mathematics 4 Science China. Mathematics 3 International Journal of Heat and Mass Transfer 3 Calcolo 3 Journal of Computational Mathematics 3 Applied Mathematical Modelling 3 SIAM Journal on Scientific Computing 3 Electronic Research Archive 2 International Journal of Modern Physics B 2 Discrete Mathematics 2 International Journal for Numerical Methods in Fluids 2 Journal of Computational Physics 2 Journal of Fluid Mechanics 2 Applied Mathematics and Computation 2 Journal of Optimization Theory and Applications 2 Numerische Mathematik 2 Communications in Applied Numerical Methods 2 Applications of Mathematics 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Numerical Mathematics: Theory, Methods and Applications 2 East Asian Journal on Applied Mathematics 2 Communications on Applied Mathematics and Computation 1 Applicable Analysis 1 Electronics Letters 1 Houston Journal of Mathematics 1 International Journal of Mechanical Sciences 1 Journal of Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Periodica Mathematica Hungarica 1 Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques 1 International Journal for Numerical Methods in Engineering 1 Journal of the American Statistical Association 1 Mechanics Research Communications 1 RAIRO. Recherche Opérationnelle 1 SIAM Journal on Computing 1 Mathematica Numerica Sinica 1 Finite Elements in Analysis and Design 1 COMPEL 1 Applied Mathematics Letters 1 Signal Processing 1 Panamerican Mathematical Journal 1 Numerical Algorithms 1 Computational Mathematics and Mathematical Physics 1 International Journal of Computer Mathematics 1 Journal of Physics A: Mathematical and General 1 SIAM Journal on Applied Mathematics 1 Neurocomputing 1 Russian Mathematics 1 Communications in Numerical Methods in Engineering 1 Advances in Computational Mathematics 1 Journal of Geodesy 1 Journal of Nonparametric Statistics 1 Mathematical Problems in Engineering 1 Mathematical Inequalities & Applications 1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 1 Physica Scripta 1 Scientia Iranica 1 Nonlinear Analysis. Modelling and Control 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Discrete and Continuous Dynamical Systems. Series B 1 International Journal of Fracture 1 Iranian Journal of Fuzzy Systems 1 Journal of Applied Functional Analysis 1 Frontiers of Mathematics in China 1 Communications in Computational Physics 1 International Journal of Numerical Analysis and Modeling. Series B 1 Journal of Applied Analysis and Computation 1 Communications in Mathematics and Statistics 1 Annals of Applied Mathematics 1 Results in Applied Mathematics
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### Fields

 128 Numerical analysis (65-XX) 85 Partial differential equations (35-XX) 51 Fluid mechanics (76-XX) 17 Mechanics of deformable solids (74-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Optics, electromagnetic theory (78-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Potential theory (31-XX) 4 Combinatorics (05-XX) 4 Computer science (68-XX) 4 Quantum theory (81-XX) 4 Biology and other natural sciences (92-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Operations research, mathematical programming (90-XX) 2 Special functions (33-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX)

### Citations contained in zbMATH Open

131 Publications have been cited 1,954 times in 1,138 Documents Cited by Year
Finite element interpolation of nonsmooth functions satisfying boundary conditions. Zbl 0696.65007
Scott, L. Ridgway; Zhang, Shangyou
1990
A new family of stable mixed finite elements for the 3D Stokes equations. Zbl 1085.76042
Zhang, Shangyou
2005
A weak Galerkin finite element method for the Maxwell equations. Zbl 1327.65220
Mu, Lin; Wang, Junping; Ye, Xiu; Zhang, Shangyou
2015
An introduction to computational nanomechanics and materials. Zbl 1079.74506
Liu, W. K.; Karpov, E. G.; Zhang, S.; Park, H. S.
2004
A $$C^0$$-weak Galerkin finite element method for the biharmonic equation. Zbl 1305.65233
Mu, Lin; Wang, Junping; Ye, Xiu; Zhang, Shangyou
2014
Quadratic divergence-free finite elements on Powell–Sabin tetrahedral grids. Zbl 1232.65151
Zhang, Shangyou
2011
Divergence-free finite elements on tetrahedral grids for $$k\geq 6$$. Zbl 1410.76204
Zhang, Shangyou
2011
An improved estimator of the density function at the boundary. Zbl 0994.62029
Zhang, S.; Karunamuni, R. J.; Jones, M. C.
1999
On the P1 Powell-Sabin divergence-free finite element for the Stokes equations. Zbl 1174.65039
Zhang, Shangyou
2008
A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids. Zbl 1308.74148
Hu, Jun; Zhang, ShangYou
2015
A weak Galerkin finite element method for singularly perturbed convection-diffusion-reaction problems. Zbl 1448.65239
Lin, Runchang; Ye, Xiu; Zhang, Shangyou; Zhu, Peng
2018
A family of 3D continuously differentiable finite elements on tetrahedral grids. Zbl 1205.76164
Zhang, Shangyou
2009
A family of $$Q_{k+1,k}\times Q_{k,k+1}$$ divergence-free finite elements on rectangular grids. Zbl 1406.76055
Zhang, Shangyou
2009
Successive subdivisions of tetrahedra and multigrid methods on tetrahedral meshes. Zbl 0855.65124
Zhang, Shangyou
1995
A new divergence-free interpolation operator with applications to the Darcy-Stokes-Brinkman equations. Zbl 1352.76071
Xu, Xuejun; Zhang, Shangyou
2010
Finite element approximations of symmetric tensors on simplicial grids in $$\mathbb{R}^n$$: the lower order case. Zbl 1348.65164
Hu, Jun; Zhang, Shangyou
2016
A simple conforming mixed finite element for linear elasticity on rectangular grids in any space dimension. Zbl 1296.65159
Hu, Jun; Man, Hongying; Zhang, Shangyou
2014
The lowest order differentiable finite element on rectangular grids. Zbl 1263.65115
Hu, Jun; Huang, Yunqing; Zhang, Shangyou
2011
Any AND-OR formula of size $$N$$ can be evaluated in time $$N^{1/2+o(1)}$$ on a quantum computer. Zbl 1207.68151
Ambainis, A.; Childs, A. M.; Reichardt, B. W.; Špalek, R.; Zhang, S.
2010
On the full $$C_1$$-$$Q_k$$ finite element spaces on rectangles and cuboids. Zbl 1262.65134
Zhang, Shangyou
2010
Optimal order multigrid methods for solving exterior boundary value problems. Zbl 0805.65113
Hsiao, George C.; Zhang, Shangyou
1994
The minimal conforming $$H^{k}$$ finite element spaces on $$\mathbb R^{n}$$ rectangular grids. Zbl 1307.65167
Hu, Jun; Zhang, Shangyou
2015
An improved product construction for large sets of Kirkman triple systems. Zbl 1012.05034
Zhang, S.; Zhu, L.
2003
Stability and approximability of the $$\mathcal P_{1}-\mathcal P_{0}$$ element for Stokes equations. Zbl 1204.76020
Qin, Jinshui; Zhang, Shangyou
2007
A stabilizer-free weak Galerkin finite element method on polytopal meshes. Zbl 1434.65285
Ye, Xiu; Zhang, Shangyou
2020
Higher-dimensional nonnested multigrid methods. Zbl 0772.65077
Scott, L. Ridgway; Zhang, Shangyou
1992
A C1-P2 finite element without nodal basis. Zbl 1145.65102
Zhang, Shangyou
2008
A weak Galerkin finite element scheme for the Cahn-Hilliard equation. Zbl 1420.65128
Wang, Junping; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou
2019
Transitive resolvable idempotent symmetric quasigroups and large sets of Kirkman triple systems. Zbl 0994.05032
Zhang, S.; Zhu, L.
2002
A lowest order divergence-free finite element on rectangular grids. Zbl 1226.65093
Huang, Yunqing; Zhang, Shangyou
2011
Wilson’s element for the Reissner-Mindlin plate. Zbl 0847.73070
Zhang, Zhimin; Zhang, Shangyou
1994
Optimal-order nonnested multigrid methods for solving finite element equations. I: On quasi-uniform meshes. Zbl 0703.65068
Zhang, Shangyou
1990
A conforming discontinuous Galerkin finite element method. II. Zbl 1465.65151
Ye, Xiu; Zhang, Shangyou
2020
On the interaction of a collapsing cavity and a compliant wall. Zbl 0718.76025
Duncan, J. H.; Zhang, S.
1991
An immediate analysis for global superconvergence for integrodifferential equations. Zbl 0902.65090
Lin, Q.; Zhang, S.
1997
An optimal order multigrid method for biharmonic, $$C^ 1$$ finite element equations. Zbl 0667.65089
Zhang, Shangyou
1989
Chaotic dynamic analysis of viscoelastic plates. Zbl 0984.74032
Sun, Y. X.; Zhang, S. Y.
2001
A conforming discontinuous Galerkin finite element method. Zbl 1465.65150
Ye, Xiu; Zhang, Shangyou
2020
Supercloseness of the divergence-free finite element solutions on rectangular grids. Zbl 1278.65180
Huang, Yunqing; Zhang, Shangyou
2013
Analytic representation of finite quantum systems. Zbl 1064.81073
Zhang, S.; Vourdas, A.
2005
Optimal-order nonnested multigrid methods for solving finite element equations. II: On non-quasi-uniform meshes. Zbl 0725.65035
Zhang, Shangyou
1990
A canonical construction of $${H^m}$$-nonconforming triangular finite elements. Zbl 1399.65326
Hu, Jun; Zhang, Shangyou
2017
Optimal-order nonnested multigrid methods for solving finite element equations. III: On degenerate meshes. Zbl 0824.65124
Zhang, Shangyou
1995
Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations. Zbl 07328855
Yang, Yin; Wang, Jindi; Zhang, Shangyou; Tohidi, Emran
2020
A family of differentiable finite elements on simplicial grids in four space dimensions. Zbl 1374.65198
Zhang, Shangyou
2016
Nonconforming finite element methods on quadrilateral meshes. Zbl 1310.65147
Hu, Jun; Zhang, Shangyou
2013
On the optimal convergence rate of a Robin-Robin domain decomposition method. Zbl 1313.65289
Chen, Wenbin; Xu, Xuejun; Zhang, Shangyou
2014
On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation. Zbl 1065.65135
Zhang, Shangyou
2004
Une méthode d’optimisation non linéaire en variables mixtes pour la conception de procédés. (A nonlinear optimization method in mixed variables for the design of processes). Zbl 0656.90071
Yuan, X.; Zhang, S.; Pibouleau, L.; Domenech, S.
1988
Large deflection of a rectangular magnetoelectroelastic thin plate. Zbl 1272.74416
Xue, C. X.; Pan, E.; Zhang, S. Y.; Chu, H. J.
2011
A meshfree method for incompressible fluid dynamics problems. Zbl 1032.76658
Tsukanov, I.; Shapiro, V.; Zhang, S.
2003
On the uniform convergence of the weak Galerkin finite element method for a singularly-perturbed biharmonic equation. Zbl 1434.65247
Cui, Ming; Zhang, Shangyou
2020
Algorithm for determining the volatility function in the Black-Scholes model. Zbl 1437.91430
Isakov, V. M.; Kabanikhin, S. I.; Shananin, A. A.; Shishlenin, M. A.; Zhang, S.
2019
Treatments of discontinuity and bubble functions in the multigrid method. Zbl 0870.65111
Zhang, Shangyou; Zhang, Zhimin
1997
Derivative superconvergence of rectangular finite elements for the Reissner-Mindlin plate. Zbl 0891.73071
Zhang, Zhimin; Zhang, Shangyou
1996
A discrete divergence free weak Galerkin finite element method for the Stokes equations. Zbl 1378.76051
Mu, Lin; Wang, Junping; Ye, Xiu; Zhang, Shangyou
2018
A P4 bubble enriched P3 divergence-free finite element on triangular grids. Zbl 1397.65298
Zhang, Shangyou
2017
Implementing and using high-order finite element methods. Zbl 0812.76042
Bagheri, Babak; Scott, L. Ridgway; Zhang, Shangyou
1994
Film evaporation of a spherical droplet over a hot surface: fluid mechanics and heat/mass transfer analysis. Zbl 0717.76121
Zhang, S.; Gogos, G.
1991
A generalized BPX multigrid framework covering nonnested V-cycle methods. Zbl 1121.65126
Duan, Huo-Yuan; Gao, Shao-Qin; Tan, Roger C. E.; Zhang, Shangyou
2007
Graph connectivity and Wiener index. Zbl 1150.05327
Gutman, I.; Zhang, S.
2006
A direct global superconvergence analysis for Sobolev and viscoelasticity type equations. Zbl 0902.65034
Lin, Q.; Zhang, S.
1997
Stabilizer-free weak Galerkin methods for monotone quasilinear elliptic PDEs. Zbl 1451.65207
Ye, Xiu; Zhang, Shangyou; Zhu, Yunrong
2020
Spectral collocation methods for nonlinear coupled time fractional Nernst-Planck equations in two dimensions and its convergence analysis. Zbl 1442.65300
Yang, Yin; Qiao, Wanying; Wang, Jindi; Zhang, Shangyou
2019
A stabilizer-free, pressure-robust, and superconvergence weak Galerkin finite element method for the Stokes equations on polytopal mesh. Zbl 07379630
Mu, Lin; Ye, Xiu; Zhang, Shangyou
2021
Multigrid computation of vector potentials. Zbl 0860.65125
Monk, Peter; Zhang, Shangyou
1995
Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems. Zbl 0876.93008
Zhang, S. Y.; Mizukami, K.; Wu, H. S.
1996
Features and partial derivatives of Bertalanffy-Richards growth model in forestry. Zbl 1047.92045
Lei, Y. C.; Zhang, S. Y.
2004
Discrete maximum-norm stability of a linearized second-order finite difference scheme for Allen-Cahn equation. Zbl 1399.65211
Hou, T.; Wang, K.; Xiong, Y.; Xiao, X.; Zhang, Sh.
2017
On the selective local stabilization of the mixed Q1-P0 element. Zbl 1130.65109
Qin, Jinshui; Zhang, Shangyou
2007
A new approach for solving Stokes systems arising from a distributive relaxation method. Zbl 1221.65301
Bacuta, Constantin; Vassilevski, Panayot S.; Zhang, Shangyou
2011
A superconvergence of the Morley element via postprocessing. Zbl 1278.65179
Huang, Jianguo; Huang, Xuehai; Zhang, Shangyou
2013
New mixed elements for Maxwell equations. Zbl 1447.78015
Duan, Huoyuan; Du, Zhijie; Liu, Wei; Zhang, Shangyou
2019
Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method. Zbl 1048.80009
Xu, B. Q.; Shen, Z. H.; Lu, J.; Ni, X. W.; Zhang, S. Y.
2003
A family of 3D $$H^2$$-nonconforming tetrahedral finite elements for the biharmonic equation. Zbl 1446.65171
Hu, Jun; Tian, Shudan; Zhang, Shangyou
2020
Approximations of two-dimensional mean field games with nonsymmetric controls. Zbl 1428.49033
Shaydurov, V.; Zhang, S.; Kornienko, V.
2020
A new $$P_1$$ weak Galerkin method for the biharmonic equation. Zbl 1427.65342
Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin
2020
Conforming and nonconforming harmonic finite elements. Zbl 1434.65275
Sorokina, Tatyana; Zhang, Shangyou
2020
New error estimates of nonconforming mixed finite element methods for the Stokes problem. Zbl 1314.65143
Li, Mingxia; Mao, Shipeng; Zhang, Shangyou
2014
High order hierarchical divergence-free constrained transport $$H\left({div} \right)$$ finite element method for magnetic induction equation. Zbl 1399.65243
Cai, Wei; Hu, Jun; Zhang, Shangyou
2017
$$C_0P_2-P_0$$ Stokes finite element pair on sub-hexahedron tetrahedral grids. Zbl 1408.76374
Zhang, Shangyou; Zhang, Shuo
2017
Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements. Zbl 1128.65100
Zhang, Shangyou
2007
A weak Galerkin least-squares finite element method for div-curl systems. Zbl 1398.65306
Li, Jichun; Ye, Xiu; Zhang, Shangyou
2018
Development of a $${P}_2$$ element with optimal $${L}^2$$ convergence for biharmonic equation. Zbl 1418.65181
Mu, Lin; Ye, Xiu; Zhang, Shangyou
2019
A Jacobi collocation method for the fractional Ginzburg-Landau differential equation. Zbl 07409024
Yang, Yin; Tao, Jianyong; Zhang, Shangyou; Sivtsev, Petr V.
2020
A family of optimal Lagrange elements for Maxwell’s equations. Zbl 1415.65254
Duan, Huoyuan; Liu, Wei; Ma, Junhua; Tan, Roger C. E.; Zhang, Shangyou
2019
Nonsingular kernel boundary integral and finite element coupling method. Zbl 1417.65210
Xu, Liwei; Zhang, Shangyou; Hsiao, George C.
2019
A locking-free weak Galerkin finite element method for Reissner-Mindlin plate on polygonal meshes. Zbl 1447.65167
Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin
2020
An error analysis method SPP-BEAM and a construction guideline of nonconforming finite elements for fourth order elliptic problems. Zbl 1463.65110
Hu, Jun; Zhang, Shangyou
2020
A stabilizer free weak Galerkin method for the biharmonic equation on polytopal meshes. Zbl 1452.65362
Ye, Xiu; Zhang, Shangyou
2020
The simplest nonconforming mixed finite element method for linear elasticity in the symmetric formulation on $$n$$-rectangular grids. Zbl 1443.65338
Hu, Jun; Man, Hongying; Wang, Jianye; Zhang, Shangyou
2016
A stabilizer-free pressure-robust finite element method for the Stokes equations. Zbl 1473.65323
Ye, Xiu; Zhang, Shangyou
2021
A stabilizer free weak Galerkin finite element method on polytopal mesh. II. Zbl 1475.65205
Ye, Xiu; Zhang, Shangyou
2021
The Euler-Lagrange approximation of the mean field game for the planning problem. Zbl 1466.65080
Shaydurov, V.; Kornienko, V.; Zhang, S.
2020
A heat transfer model for thermal fluctuations in a thin slider/disk air bearing. Zbl 0954.76502
Zhang, S.; Bogy, D. B.
1999
Unsteady conservative streamfunction coordinate formulation: 1-D isentropic flow. Zbl 0810.76051
Barron, R. M.; An, C-F.; Zhang, S.
1994
A 3D conforming-nonconforming mixed finite element for solving symmetric stress Stokes equations. Zbl 1378.76055
Zhang, Min; Zhang, Shangyou
2017
A postprocessed flux conserving finite element solution. Zbl 1384.65085
Zhang, Shangyou; Zhang, Zhimin; Zou, Qingsong
2017
Singularity of dynamic stress fields around an interface crack between viscoelastic bodies. Zbl 1187.74089
Wei, P. J.; Zhang, S. Y.
2004
Weak Galerkin and continuous Galerkin coupled finite element methods for the Stokes-Darcy interface problem. Zbl 1473.65313
Peng, Hui; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou
2020
A stabilizer-free, pressure-robust, and superconvergence weak Galerkin finite element method for the Stokes equations on polytopal mesh. Zbl 07379630
Mu, Lin; Ye, Xiu; Zhang, Shangyou
2021
A stabilizer-free pressure-robust finite element method for the Stokes equations. Zbl 1473.65323
Ye, Xiu; Zhang, Shangyou
2021
A stabilizer free weak Galerkin finite element method on polytopal mesh. II. Zbl 1475.65205
Ye, Xiu; Zhang, Shangyou
2021
A stabilizer free weak Galerkin finite element method on polytopal mesh. III. Zbl 1475.65172
Ye, Xiu; Zhang, Shangyou
2021
A conforming discontinuous Galerkin finite element method on rectangular partitions. Zbl 1478.65122
Feng, Yue; Liu, Yujie; Wang, Ruishu; Zhang, Shangyou
2021
Trivariate interpolated Galerkin finite elements for the Poisson equation. Zbl 1477.65247
Sorokina, Tatyana; Zhang, Shangyou
2021
A stabilizer-free weak Galerkin finite element method on polytopal meshes. Zbl 1434.65285
Ye, Xiu; Zhang, Shangyou
2020
A conforming discontinuous Galerkin finite element method. II. Zbl 1465.65151
Ye, Xiu; Zhang, Shangyou
2020
A conforming discontinuous Galerkin finite element method. Zbl 1465.65150
Ye, Xiu; Zhang, Shangyou
2020
Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations. Zbl 07328855
Yang, Yin; Wang, Jindi; Zhang, Shangyou; Tohidi, Emran
2020
On the uniform convergence of the weak Galerkin finite element method for a singularly-perturbed biharmonic equation. Zbl 1434.65247
Cui, Ming; Zhang, Shangyou
2020
Stabilizer-free weak Galerkin methods for monotone quasilinear elliptic PDEs. Zbl 1451.65207
Ye, Xiu; Zhang, Shangyou; Zhu, Yunrong
2020
A family of 3D $$H^2$$-nonconforming tetrahedral finite elements for the biharmonic equation. Zbl 1446.65171
Hu, Jun; Tian, Shudan; Zhang, Shangyou
2020
Approximations of two-dimensional mean field games with nonsymmetric controls. Zbl 1428.49033
Shaydurov, V.; Zhang, S.; Kornienko, V.
2020
A new $$P_1$$ weak Galerkin method for the biharmonic equation. Zbl 1427.65342
Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin
2020
Conforming and nonconforming harmonic finite elements. Zbl 1434.65275
Sorokina, Tatyana; Zhang, Shangyou
2020
A Jacobi collocation method for the fractional Ginzburg-Landau differential equation. Zbl 07409024
Yang, Yin; Tao, Jianyong; Zhang, Shangyou; Sivtsev, Petr V.
2020
A locking-free weak Galerkin finite element method for Reissner-Mindlin plate on polygonal meshes. Zbl 1447.65167
Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin
2020
An error analysis method SPP-BEAM and a construction guideline of nonconforming finite elements for fourth order elliptic problems. Zbl 1463.65110
Hu, Jun; Zhang, Shangyou
2020
A stabilizer free weak Galerkin method for the biharmonic equation on polytopal meshes. Zbl 1452.65362
Ye, Xiu; Zhang, Shangyou
2020
The Euler-Lagrange approximation of the mean field game for the planning problem. Zbl 1466.65080
Shaydurov, V.; Kornienko, V.; Zhang, S.
2020
Weak Galerkin and continuous Galerkin coupled finite element methods for the Stokes-Darcy interface problem. Zbl 1473.65313
Peng, Hui; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou
2020
The weak Galerkin finite element method for the transport-reaction equation. Zbl 1436.65193
Zhang, Tie; Zhang, Shangyou
2020
A conforming discontinuous Galerkin finite element method. III. Zbl 1484.65308
Ye, Xiu; Zhang, Shangyou
2020
Conforming harmonic finite elements on the Hsieh-Clough-Tocher split of a triangle. Zbl 1465.65146
Sorokina, Tatyana; Zhang, Shangyou
2020
The weak Galerkin finite element method for the symmetric hyperbolic systems. Zbl 1428.65051
Zhang, Tie; Zhang, Shangyou
2020
Modified weak Galerkin method with weakly imposed boundary condition for convection-dominated diffusion equations. Zbl 1446.76128
Gao, Fuzheng; Zhang, Shangyou; Zhu, Peng
2020
An inequality involving a triangle and an interior point and its application. Zbl 1444.51003
Sorokina, Tatyana; Zhang, Shangyou
2020
A weak Galerkin finite element scheme for the Cahn-Hilliard equation. Zbl 1420.65128
Wang, Junping; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou
2019
Algorithm for determining the volatility function in the Black-Scholes model. Zbl 1437.91430
Isakov, V. M.; Kabanikhin, S. I.; Shananin, A. A.; Shishlenin, M. A.; Zhang, S.
2019
Spectral collocation methods for nonlinear coupled time fractional Nernst-Planck equations in two dimensions and its convergence analysis. Zbl 1442.65300
Yang, Yin; Qiao, Wanying; Wang, Jindi; Zhang, Shangyou
2019
New mixed elements for Maxwell equations. Zbl 1447.78015
Duan, Huoyuan; Du, Zhijie; Liu, Wei; Zhang, Shangyou
2019
Development of a $${P}_2$$ element with optimal $${L}^2$$ convergence for biharmonic equation. Zbl 1418.65181
Mu, Lin; Ye, Xiu; Zhang, Shangyou
2019
A family of optimal Lagrange elements for Maxwell’s equations. Zbl 1415.65254
Duan, Huoyuan; Liu, Wei; Ma, Junhua; Tan, Roger C. E.; Zhang, Shangyou
2019
Nonsingular kernel boundary integral and finite element coupling method. Zbl 1417.65210
Xu, Liwei; Zhang, Shangyou; Hsiao, George C.
2019
A cubic $$H^3$$-nonconforming finite element. Zbl 1449.65315
Hu, Jun; Zhang, Shangyou
2019
The finite difference approximation preserving conjugate properties of the mean-field game equations. Zbl 1418.91070
Shaydurov, V.; Zhang, S.; Karepova, E.
2019
A weak Galerkin finite element method for singularly perturbed convection-diffusion-reaction problems. Zbl 1448.65239
Lin, Runchang; Ye, Xiu; Zhang, Shangyou; Zhu, Peng
2018
A discrete divergence free weak Galerkin finite element method for the Stokes equations. Zbl 1378.76051
Mu, Lin; Wang, Junping; Ye, Xiu; Zhang, Shangyou
2018
A weak Galerkin least-squares finite element method for div-curl systems. Zbl 1398.65306
Li, Jichun; Ye, Xiu; Zhang, Shangyou
2018
Financial bubbles existence in the Cantor-Lippman model for continuous time. Zbl 1417.91480
Shananin, A. A.; Vashchenko, M. P.; Zhang, Sh.
2018
A canonical construction of $${H^m}$$-nonconforming triangular finite elements. Zbl 1399.65326
Hu, Jun; Zhang, Shangyou
2017
A P4 bubble enriched P3 divergence-free finite element on triangular grids. Zbl 1397.65298
Zhang, Shangyou
2017
Discrete maximum-norm stability of a linearized second-order finite difference scheme for Allen-Cahn equation. Zbl 1399.65211
Hou, T.; Wang, K.; Xiong, Y.; Xiao, X.; Zhang, Sh.
2017
High order hierarchical divergence-free constrained transport $$H\left({div} \right)$$ finite element method for magnetic induction equation. Zbl 1399.65243
Cai, Wei; Hu, Jun; Zhang, Shangyou
2017
$$C_0P_2-P_0$$ Stokes finite element pair on sub-hexahedron tetrahedral grids. Zbl 1408.76374
Zhang, Shangyou; Zhang, Shuo
2017
A 3D conforming-nonconforming mixed finite element for solving symmetric stress Stokes equations. Zbl 1378.76055
Zhang, Min; Zhang, Shangyou
2017
A postprocessed flux conserving finite element solution. Zbl 1384.65085
Zhang, Shangyou; Zhang, Zhimin; Zou, Qingsong
2017
Finite element approximations of symmetric tensors on simplicial grids in $$\mathbb{R}^n$$: the lower order case. Zbl 1348.65164
Hu, Jun; Zhang, Shangyou
2016
A family of differentiable finite elements on simplicial grids in four space dimensions. Zbl 1374.65198
Zhang, Shangyou
2016
The simplest nonconforming mixed finite element method for linear elasticity in the symmetric formulation on $$n$$-rectangular grids. Zbl 1443.65338
Hu, Jun; Man, Hongying; Wang, Jianye; Zhang, Shangyou
2016
Stable $$Q_k-Q_{k-1}$$ mixed finite elements with discontinuous pressure. Zbl 1331.76074
Zhang, Shangyou; Mu, Mo
2016
A weak Galerkin finite element method for the Maxwell equations. Zbl 1327.65220
Mu, Lin; Wang, Junping; Ye, Xiu; Zhang, Shangyou
2015
A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids. Zbl 1308.74148
Hu, Jun; Zhang, ShangYou
2015
The minimal conforming $$H^{k}$$ finite element spaces on $$\mathbb R^{n}$$ rectangular grids. Zbl 1307.65167
Hu, Jun; Zhang, Shangyou
2015
A unified mortar condition for nonconforming finite elements. Zbl 1309.65138
Wang, Chunmei; Zhang, Shangyou; Chen, Jinru
2015
A $$C^0$$-weak Galerkin finite element method for the biharmonic equation. Zbl 1305.65233
Mu, Lin; Wang, Junping; Ye, Xiu; Zhang, Shangyou
2014
A simple conforming mixed finite element for linear elasticity on rectangular grids in any space dimension. Zbl 1296.65159
Hu, Jun; Man, Hongying; Zhang, Shangyou
2014
On the optimal convergence rate of a Robin-Robin domain decomposition method. Zbl 1313.65289
Chen, Wenbin; Xu, Xuejun; Zhang, Shangyou
2014
New error estimates of nonconforming mixed finite element methods for the Stokes problem. Zbl 1314.65143
Li, Mingxia; Mao, Shipeng; Zhang, Shangyou
2014
Solving negative order equations by the multigrid method via variable substitution. Zbl 1307.65172
Hsiao, George C.; Xu, Liwei; Zhang, Shangyou
2014
Supercloseness of the divergence-free finite element solutions on rectangular grids. Zbl 1278.65180
Huang, Yunqing; Zhang, Shangyou
2013
Nonconforming finite element methods on quadrilateral meshes. Zbl 1310.65147
Hu, Jun; Zhang, Shangyou
2013
A superconvergence of the Morley element via postprocessing. Zbl 1278.65179
Huang, Jianguo; Huang, Xuehai; Zhang, Shangyou
2013
An iterative method based on equation decomposition for the fourth-order singular perturbation problem. Zbl 1288.65165
Han, Houde; Huang, Zhongyi; Zhang, Shangyou
2013
A divergence-free finite element method for a type of 3D Maxwell equations. Zbl 1241.78043
Huang, Jianguo; Zhang, Shangyou
2012
Quadratic divergence-free finite elements on Powell–Sabin tetrahedral grids. Zbl 1232.65151
Zhang, Shangyou
2011
Divergence-free finite elements on tetrahedral grids for $$k\geq 6$$. Zbl 1410.76204
Zhang, Shangyou
2011
The lowest order differentiable finite element on rectangular grids. Zbl 1263.65115
Hu, Jun; Huang, Yunqing; Zhang, Shangyou
2011
A lowest order divergence-free finite element on rectangular grids. Zbl 1226.65093
Huang, Yunqing; Zhang, Shangyou
2011
Large deflection of a rectangular magnetoelectroelastic thin plate. Zbl 1272.74416
Xue, C. X.; Pan, E.; Zhang, S. Y.; Chu, H. J.
2011
A new approach for solving Stokes systems arising from a distributive relaxation method. Zbl 1221.65301
Bacuta, Constantin; Vassilevski, Panayot S.; Zhang, Shangyou
2011
A new divergence-free interpolation operator with applications to the Darcy-Stokes-Brinkman equations. Zbl 1352.76071
Xu, Xuejun; Zhang, Shangyou
2010
Any AND-OR formula of size $$N$$ can be evaluated in time $$N^{1/2+o(1)}$$ on a quantum computer. Zbl 1207.68151
Ambainis, A.; Childs, A. M.; Reichardt, B. W.; Špalek, R.; Zhang, S.
2010
On the full $$C_1$$-$$Q_k$$ finite element spaces on rectangles and cuboids. Zbl 1262.65134
Zhang, Shangyou
2010
Zeros in analytic representations of finite quantum systems on a torus. Zbl 1198.81112
Tubani, M.; Vourdas, A.; Zhang, S.
2010
A family of 3D continuously differentiable finite elements on tetrahedral grids. Zbl 1205.76164
Zhang, Shangyou
2009
A family of $$Q_{k+1,k}\times Q_{k,k+1}$$ divergence-free finite elements on rectangular grids. Zbl 1406.76055
Zhang, Shangyou
2009
On the P1 Powell-Sabin divergence-free finite element for the Stokes equations. Zbl 1174.65039
Zhang, Shangyou
2008
A C1-P2 finite element without nodal basis. Zbl 1145.65102
Zhang, Shangyou
2008
Stability and approximability of the $$\mathcal P_{1}-\mathcal P_{0}$$ element for Stokes equations. Zbl 1204.76020
Qin, Jinshui; Zhang, Shangyou
2007
A generalized BPX multigrid framework covering nonnested V-cycle methods. Zbl 1121.65126
Duan, Huo-Yuan; Gao, Shao-Qin; Tan, Roger C. E.; Zhang, Shangyou
2007
On the selective local stabilization of the mixed Q1-P0 element. Zbl 1130.65109
Qin, Jinshui; Zhang, Shangyou
2007
Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements. Zbl 1128.65100
Zhang, Shangyou
2007
Computing porosity of cancellous bone using ultrasonic waves. Zbl 1113.92033
Gilbert, Robert P.; Xu, Yongzhi; Zhang, Shangyou
2007
Graph connectivity and Wiener index. Zbl 1150.05327
Gutman, I.; Zhang, S.
2006
A new family of stable mixed finite elements for the 3D Stokes equations. Zbl 1085.76042
Zhang, Shangyou
2005
Analytic representation of finite quantum systems. Zbl 1064.81073
Zhang, S.; Vourdas, A.
2005
Axisymmetric finite element solution of non-isothermal parallel-plate flow. Zbl 1088.76028
Zhang, Shangyou; Olagunju, David O.
2005
Yang, Yuanxi; Zhang, S.
2005
An introduction to computational nanomechanics and materials. Zbl 1079.74506
Liu, W. K.; Karpov, E. G.; Zhang, S.; Park, H. S.
2004
On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation. Zbl 1065.65135
Zhang, Shangyou
2004
Features and partial derivatives of Bertalanffy-Richards growth model in forestry. Zbl 1047.92045
Lei, Y. C.; Zhang, S. Y.
2004
Singularity of dynamic stress fields around an interface crack between viscoelastic bodies. Zbl 1187.74089
Wei, P. J.; Zhang, S. Y.
2004
Two-dimensional transient thermal analysis of diamond/Si structures heated by a pulsed circular Gaussian laser beam. Zbl 1052.74005
Mi, X. B.; Gao, H. D.; Zhang, S. Y.
2004
An improved product construction for large sets of Kirkman triple systems. Zbl 1012.05034
Zhang, S.; Zhu, L.
2003
A meshfree method for incompressible fluid dynamics problems. Zbl 1032.76658
Tsukanov, I.; Shapiro, V.; Zhang, S.
2003
Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method. Zbl 1048.80009
Xu, B. Q.; Shen, Z. H.; Lu, J.; Ni, X. W.; Zhang, S. Y.
2003
Phase space methods for particles on a circle. Zbl 1062.81102
Zhang, S.; Vourdas, A.
2003
Transitive resolvable idempotent symmetric quasigroups and large sets of Kirkman triple systems. Zbl 0994.05032
Zhang, S.; Zhu, L.
2002
...and 31 more Documents
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### Cited by 1,221 Authors

 72 Zhang, Shangyou 37 Rebholz, Leo G. 30 Ye, Xiu 22 Linke, Alexander 21 Neilan, Michael 21 Praetorius, Dirk 18 Carstensen, Carsten 18 Girault, Vivette 17 Melenk, Jens Markus 16 Hu, Jun 16 Larson, Mats G. 16 Zhai, Qilong 15 Guzmán, Johnny 15 Li, Jichun 15 Mu, Lin 14 Burman, Erik 14 Chen, Long 14 Huang, Yunqing 14 Karkulik, Michael 14 Wang, Junping 13 Duan, Huoyuan 13 Wohlmuth, Barbara I. 13 Xu, Jinchao 11 Brenner, Susanne Cecelia 11 Feischl, Michael 11 Führer, Thomas 11 Gatica, Gabriel N. 11 Hansbo, Peter 11 Huang, Xuehai 11 Scott, Larkin Ridgway 11 Xie, Xiaoping 11 Zhang, Shuo 10 Nochetto, Ricardo Horacio 10 Salgado, Abner J. 10 Sinha, Rajen Kumar 10 Wang, Ruishu 10 Wu, Haijun 10 Xie, Hehu 9 He, Yinnian 9 Merdon, Christian 9 Wang, Chunmei 9 Wang, Xiaoshen 9 Xu, Xuejun 9 Xu, Yifeng 9 Yan, Ningning 9 Zhu, Peng 8 Korotov, Sergey 8 Meng, Zhaoliang 8 Rubino, Samuele 8 Shi, Zhongci 8 Stevenson, Rob P. 8 Tan, Roger C. E. 8 Veeser, Andreas 8 Xiao, Mengying 8 Zhang, Zhimin 8 Zou, Jun 7 Ainsworth, Mark 7 Chen, Jinru 7 Chen, Shaochun 7 Faustmann, Markus 7 Feng, Minfu 7 Gao, Fuzheng 7 Hiptmair, Ralf 7 Hussain, Saqib 7 Ku, Jaeun 7 Lamichhane, Bishnu Prasad 7 Luo, Zhongxuan 7 Mao, Shipeng 7 Nicaise, Serge 7 Otárola, Enrique 7 Park, Eun-Jae 7 Peterseim, Daniel 7 Wilson, Nicholas E. 6 Al-Taweel, Ahmed 6 Badia, Santiago 6 Gedicke, Joscha 6 Guillén González, Francisco M. 6 John, Volker 6 Křížek, Michal 6 Liu, Steve Wenbin 6 Novo, Julia 6 Sayas, Francisco-Javier 6 Tobiska, Lutz 6 Wu, Shuonan 6 Yotov, Ivan 6 Zhong, Liuqiang 5 Ahmed, Naveed 5 Apel, Thomas 5 Bi, Chunjia 5 Chacón Rebollo, Tomás 5 Chen, Huangxin 5 Cui, Jintao 5 Demlow, Alan 5 Diening, Lars 5 Gallistl, Dietmar 5 García-Archilla, Bosco 5 Georgoulis, Emmanuil H. 5 Graham, Ivan G. 5 Hecht, Frédéric 5 Kreuzer, Christian ...and 1,121 more Authors
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### Cited in 117 Serials

 92 Numerische Mathematik 91 Journal of Computational and Applied Mathematics 89 Mathematics of Computation 85 Journal of Scientific Computing 70 Computers & Mathematics with Applications 59 SIAM Journal on Numerical Analysis 55 Computer Methods in Applied Mechanics and Engineering 51 Applied Numerical Mathematics 36 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 28 SIAM Journal on Scientific Computing 27 Applied Mathematics and Computation 25 Advances in Applied Mathematics and Mechanics 21 Calcolo 20 Journal of Computational Physics 19 Numerical Methods for Partial Differential Equations 17 Advances in Computational Mathematics 17 Journal of Numerical Mathematics 16 Computational Methods in Applied Mathematics 16 Science China. Mathematics 12 International Journal for Numerical Methods in Engineering 11 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 11 Communications in Computational Physics 10 Journal of Mathematical Analysis and Applications 10 BIT 9 Numerical Functional Analysis and Optimization 9 International Journal of Computer Mathematics 9 International Journal of Numerical Analysis and Modeling 7 Applied Mathematics Letters 7 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 7 Discrete and Continuous Dynamical Systems. Series B 6 Numerical Algorithms 6 Computational and Applied Mathematics 6 Mathematical Problems in Engineering 6 Foundations of Computational Mathematics 6 Electronic Research Archive 5 Frontiers of Mathematics in China 4 Mathematical Methods in the Applied Sciences 4 Computing 4 Mathematics and Computers in Simulation 4 Applications of Mathematics 4 Computational Geosciences 4 Boundary Value Problems 4 East Asian Journal on Applied Mathematics 4 SMAI Journal of Computational Mathematics 4 Communications on Applied Mathematics and Computation 3 International Journal for Numerical Methods in Fluids 3 Journal of Computational Mathematics 3 Science in China. Series A 3 ETNA. Electronic Transactions on Numerical Analysis 3 Engineering Analysis with Boundary Elements 3 Journal of Mathematical Fluid Mechanics 3 Archives of Computational Methods in Engineering 3 Multiscale Modeling & Simulation 3 International Journal of Computational Methods 3 Results in Applied Mathematics 2 Applicable Analysis 2 Inverse Problems 2 Applied Mathematics and Optimization 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Constructive Approximation 2 Computational Mechanics 2 Journal of Integral Equations and Applications 2 Japan Journal of Industrial and Applied Mathematics 2 Computational Mathematics and Mathematical Physics 2 Applied Mathematical Modelling 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Computational Optimization and Applications 2 Numerical Linear Algebra with Applications 2 Computing and Visualization in Science 2 Abstract and Applied Analysis 2 Discrete Dynamics in Nature and Society 2 Engineering Computations 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Applied Mathematics and Computing 2 Oberwolfach Reports 2 Numerical Mathematics: Theory, Methods and Applications 2 Advances in Mathematical Physics 2 S$$\vec{\text{e}}$$MA Journal 2 Journal of Applied Analysis and Computation 2 AIMS Mathematics 1 Journal of Engineering Mathematics 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Mathematische Zeitschrift 1 Results in Mathematics 1 SIAM Journal on Control and Optimization 1 Zeitschrift für Analysis und ihre Anwendungen 1 Applied Mathematics and Mechanics. (English Edition) 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematicae Applicatae Sinica. English Series 1 Mathematical and Computer Modelling 1 SIAM Review 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Journal of Mathematical Imaging and Vision 1 Continuum Mechanics and Thermodynamics 1 Applied Mathematics. Series B (English Edition) 1 Fractals 1 Journal of Convex Analysis 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Discrete and Continuous Dynamical Systems 1 Vietnam Journal of Mathematics ...and 17 more Serials
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### Cited in 33 Fields

 1,050 Numerical analysis (65-XX) 555 Partial differential equations (35-XX) 328 Fluid mechanics (76-XX) 158 Mechanics of deformable solids (74-XX) 81 Optics, electromagnetic theory (78-XX) 45 Calculus of variations and optimal control; optimization (49-XX) 26 Approximations and expansions (41-XX) 12 Global analysis, analysis on manifolds (58-XX) 11 Potential theory (31-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Operator theory (47-XX) 9 Integral equations (45-XX) 9 Biology and other natural sciences (92-XX) 6 Real functions (26-XX) 6 Ordinary differential equations (34-XX) 6 Functional analysis (46-XX) 6 Probability theory and stochastic processes (60-XX) 6 Computer science (68-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Systems theory; control (93-XX) 4 Operations research, mathematical programming (90-XX) 3 General and overarching topics; collections (00-XX) 3 Relativity and gravitational theory (83-XX) 3 Geophysics (86-XX) 2 Convex and discrete geometry (52-XX) 2 Statistics (62-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)