Papers

• Lack of robustness and accuracy of many numerical schemes for phase-field simulations

J. Xu, X. Xu
Mathematical Models and Methods in Applied Sciences   (2023)

• Greedy training algorithms for neural networks and applications to PDEs

J. W. Siegel, Q. Hong, X. Jin, W. Hao
Journal of Computational Physics   (2023)

• Characterization of the Variation Spaces Corresponding to Shallow Neural Networks

J. W. Siegel, J. Xu
Constructive Approximation   (2023)

• An Interpretive Constrained Linear Model for ResNet and MgNet

J. He, J. Xu, L. Zhang, J. Zhu
Neural Networks Volume 162, Page 384-392  (2023)

• FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting

J. Zhu, J. He, L. Zhang, J. Xu
Journal of Computational Science Volume 69, 102005  (2023)

• An efficient iterative method for dynamical Ginzburg-Landau equations

Q. Hong, L. Ma, J. Xu, L. Chen
Journal of Computational Physics Volume 474, 111794  (2023)

• Integral boundary conditions in phase field models

X. Xu, L. Zhang, Y. Shi, L. Chen, J. Xu
Computers and Mathematics with Applications Volume 135, Page 1-5  (2023)

• Sharp Bounds on the Approximation Rates, Metric Entropy, and n-widths of Shallow Neural Networks

J. W. Siegel, J. Xu
Foundations of Computational Mathematics   (2022)

• Block triangular preconditioning for stochastic Galerkin method

D. Wang, B. Zheng, L. Chen, G. Lin, J. Xu
Journal of Computational and Applied Mathematics   (2022)

• Uniform Approximation Rates and Metric Entropy of Shallow Neural Networks

L. Ma, J. W. Siegel, J. Xu
Research in the Mathematical Sciences 9 (3), 46  (2022)

• Approximation Properties of Deep ReLU CNNs

J. He, L. Li, J. Xu
Research in the Mathematical Sciences 9 (3), 46  (2022)

• ReLU Deep Neural Networks from the Hierarchical Basis Perspective

J. He, L. Li, J. Xu
Computers \& Mathematics with Applications 120: 105-114  (2022)

• CNNs with Compact Activation Function

J. Wang, J. Zhu, J. Xu
Computational Science-ICCS 2022: 22nd International Conferenc   (2022)

• Extensible Structure-Informed Prediction of Formation Energy with Improved Accuracy and Usability employing Neural Networks

A. Krajewskia, J. W.Siegel, J. Xu, Z. Liu
Computational Materials Science Volume 208, 111254  (2022)

• High-Order Approximation Rates for Neural Networks with ReLU^k Activation Functions

J. W. Siegel, J. Xu
Computational and Applied Harmonic Analysis ,Volume 58, Pages 1-26   (2022)

• Extended Galerkin analysis in finite element exterior calculus

Q.Hong, Y. Li, J. Xu
Mathematics of Computation 91.335, 1077-1106   (2022)

• Meta-MgNet: Meta multigrid networks forsSolving parameterized partial differential equation

Y. Chen, B. Dong, J.Xu
Journal of Computational Physics 110996  (2022)

• Optimal convergence rates for the orthogonal greedy algorithm

J. W. Siegel, J. Xu
IEEE Transactions on Information Theory   (2022)

• New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor

Q. Hong, J. Hu, L. Ma, J. Xu
Numerische Mathematik 149 (3), 645-678   (2021)

• Helicity-Conservative Finite Element Discretization for MHD Systems

K. Hu, YJ. Lee, J. Xu
Journal of Computational Physics, Volume 436, 110284 ,  (2021)

• Multiscale and Monolithic Arbitrary Lagrangian-Eulerian Finite Element Method for a Hemodynamic Fluid-structure Interaction Problem Involving Aneurysms

W. Hao, P. Sun, J. Xu, L. Zhang
Journal of Computational Physics, Volume 433, 110181 ,  (2021)

• Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods

Q. Hong, J. Xu
Journal of Computational Mathematics, Vol.39, No.2, 283-310 ,  (2021)

• An Extended Galerkin Analysis for Elliptic Problems

Q. Hong, S Wu, J. Xu
Science China Mathematics, 64 ,  (2021)

• Finite Neuron Method and Convergence Analysis

J. Xu
Commun. Comput. Phys.Vol. 28, No. 5, pp. 1707-1745 ,  (2020)

• An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity

Q. Hong, C. Liu, J. Xu
Mathematica Numerical Sinica,, 42 (3), 298-209 ,  (2020)

• Approximation rates for neural networks with general activation functions

J.W. Siegel, J. Xu
Neural Networks ,  (2020)

• Make $\ell_1$ regularization effective in training sparse CNN

J. He, X. Jia, J. Xu, L. Zhang, L. Zhao
Computational Optimization and Applications ,  77,  163-182  (2020)

• High-order extended finite element methods for solving interface problems

Y Xiao, J Xu, F Wang
Computer Methods in Applied Mechanics and Engineering ,  364,  112964  (2020)

• A mixed discontinuous Galerkin method for linear elasticity with strongly imposed symmetry

F Wang, S Wu, J Xu
Journal of Scientific Computing ,  83 (1),  1-17  (2020)

• ReLU Deep Neural Networks and linear Finite Elements

J. He ; L. Li ; J. Xu; C. Zheng
Journal of Computational Mathematics ,  (2020)

• Robust preconditioners for poroelasticity

S Chen, Q Hong, J Xu, K Yang
Computer Methods in Applied Mechanics and Engineering ,  369, 113229,    (2020)

• Simplex-Averaged Finite Element Methods for (grad), (curl), and (div) Convection-Diffusion Problems

S Wu, J Xu
SIAM Journal on Numerical Analysis ,  58 (1),  884-906  (2020)

• Generalized Gaffney inequality and discrete compactness for discrete differential forms

J. He, K. Hu, J. Xu
Numerische Mathematik ,  143 (4),  781-795  (2019)

• A machine learning method correlating pulse pressure wave data with pregnancy

J. Chen, H. Huang, W. Hao, J. Xu
International journal for numerical methods in biomedical engineering ,  (2019)

• Randomized and Fault-Tolerant Method of Subspace Corrections

X. Hu, J. Xu, L. Zikatanov
Research in the Mathematical Sciences ,  6 (3),  29  (2019)

• MgNet: A Unified Framework of Multigrid and Convolutional Neural Network

J He, J Xu
Science China Mathematics ,  62,  1331-1354  (2019)

• On the Stability and Accuracy of Partially and Fully Implicit Schemes for Phase Field Modeling

J. Xu, Y. Li, S. Wu, A. Bousquet
Computer Methods in Applied Mechanics and Engineering ,  345,  826-853  (2019)

• New Hybridized Mixed Methods for Linear Elasticity and Optimal Multilevel Solvers

S. Gong, S. Wu, J. Xu
Numerische Mathematik ,  141 (2),  569--604  (2019)

• Numerical Simulation of An Immersed Rotating Structure in Fluid for Hemodynamic Applications

W. Leng, C. Zhang, P. Sun, B. Gao, J. Xu
Journal of Computational Science ,  30,  79-89  (2019)

• A Unified Study of Continuous and Discontinuous Galerkin Methods

Q. Hong, F. Wang, S. Wu, and J. Xu
SCIENCE CHINA Mathematics ,  62 (1),  1--32  (2019)

• Nonconforming Finite Element Spaces for 2m-th Order Partial Differential Equations on R^n Simplicial Grids When m=n+1

S. Wu, and J. Xu
Mathematics of Computation 88 (316),  531--551  (2019)

• Structure-preserving Finite Element Methods for Stationary MHD Models

K. Hu, and J. Xu
Mathematics of Computation 88 (316),  553--581  (2019)

• Error Estimates of the Classical and Improved Two-Grid Methods

W. Zhang, J. Xu, L. Zhong
Advance in Applied Mathematics and Mechanics ,  10,  785-796  (2018)

• Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods

Q. Hong, J. Xu
International Conference on Computational Science ,  9-23  (2018)

• ALE Method for a Rotating Structure Immersed in the Fluid and Its Application to the Artificial Heart Pump in Hemodynamics

P. Sun, W. Leng, C. Zhang, R. Lan, J. Xu
International Conference on Computational Science ,  9-23  (2018)

• Newton Solvers for Drift-Diffusion and Electrokinetic Equations

A Bousquet, X Hu, MS Metti, J Xu
SIAM Journal on Scientific Computing ,  40,  B982--B1006  (2018)

• Interior Penalty Mixed Finite Element Methods of Any Order in Any Dimension for Linear Elasticity with Strongly Symmetric Stress Tensor

S. Wu, S. Gong, and J. Xu
Math. Models Methods Appl. Sci. ,  27,  2711--2743  (2017)

• Algebraic Multigrid Methods

J. Xu, L. Zikatanov
Acta Numerica ,  591--721  (2017)

• Multiphase Allen-Cahn and Cahn-Hilliard Models and Their Discretizations with the Effect of Pairwise Surface Tensions

S. Wu, and J. Xu
J. Comput. Phys. ,  343,  10--32  (2017)

• A Mathematical Model of Aortic Aneurysm Formation

W. Hao, S. Gong, S. Wu, J. Xu, M. Go, A. Friedman, and D. Zhu
PloS one,  12(2),  (2017)

• Numerical Studies of a Class of Linear Solvers for Fine-scale Petroleum Reservoir Simulation

Z. Li, S. Wu, C. Zhang, J. Xu, C. Feng and X. Hu
Comput. Visual Sci. ,  18(2),  93-102  (2017)

• Analytical Decoupling Techniques for Fully Implicit Reservoir Simulation

C. Qiao, S. Wu, J. Xu, and C. Zhang
J. Comput. Phys. ,  336,  664--681  (2017)

• Stable Finite Element Methods Preserving $\nabla \cdot \varvec{B} = 0$ Exactly for MHD Models

K. Hu, Y. Ma, and J. Xu
Numer. Math.,  135(2),  371-396  (2017)

• An Error-Resilient Redundant Subspace Correction Method

T. Cui, J. Xu, and C. Zhang
Comput. Visual Sci. ,  18(2),  65--77  (2017)

• Toward Cost-Effective Reservoir Simulation Solvers on GPUs

Z. Li, S. Wu, J. Xu, and C. Zhang
Adv. Appl. Math. Mech. ,  8(6),  971--991  (2016)

• A Robust Multigrid Method for Discontinuous Galerkin Discretizations of Stokes and Linear Elasticity Equations

Q. Hong, J. Kraus, J. Xu, and L. Zikatanov
Numerische Mathematik ,  132(1),  23-49  (2016)

• A nearly optimal multigrid method for general unstructured grids

L. Gradsedyck, L. Wang and J. Xu
Numerische Mathematik ,  134(3),  637-666  (2016)

• Modeling and Simulations for Fluid and Rotating Structure Interactions

K. Yang, P. Sun, L. Wang, J. Xu, and L. Zhang
Comput. Methods. Appl. Mech. Eng. ,  311,  788--814  (2016)

• A Two-grid SA-AMG Convergence Bound that Improves When Increasing the Polynomial Degree

X. Hu, P.S. Vassilevski, and J. Xu
Numer. Linear Algebra Appl. ,  23(4),  746--771  (2016)

• Robust Preconditioners for Incompressible MHD Models

Y. Ma, K. Hu, X. Hu, and J. Xu
J. Comput. Phys. ,  316,  721--746  (2016)

• Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

B. Zheng, L. Chen, X. Hu, L. Chen, R. Nochetto, and J. Xu
J. Sci. Comput. ,  69(1),  201--226  (2016)

• Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

T. Kolev, J. Xu, and Y. Zhu
J. Sci. Comput. ,  67(1),  324--350  (2016)

• Energetically Stable Discretizations for Charge Transport and Electrokinetic Models

M.S. Metti, J. Xu, and C. Liu
J. Comput. Phys.,  306,  1--18  (2016)

• A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians

J. C. Urschel, X. Hu, J. Xu, and L. Zikatanov
J. Comp. Math.,  33,  209-226  (2015)

• On Robust and Efficient Parallel Reservoir Simulation on Tianhe-2

W. Guan, C. Qiao, H. Zhang, C. Zhang, M. Zhi, Z. Zhu, Z. Zheng, W. Ye, Y. Zhang, X. Hu, Z. Li, C. Feng, Y. Xu, J. Xu
SPE Reservoir Characterisation and Simulation Conference and Exhibition,  doi.org/10.2118/175602-MS  (2015)

• Modeling Low Salinity Waterflooding in Mineralogically Different Carbonates

C. Qiao, R.T. Johns, L. Li and J. Xu
SPE Annual Technical Conference and Exhibition,  doi:10.2118/175018-MS  (2015)

• Mechanistic Modeling of Wettability Alteration by Chemically Tuned Water Flooding in Carbonate Reservoirs

C. Qiao, L. Li, R.T. Johns and J. Xu
SPE Journal,  doi:10.2118/170966-PA  (2015)

• A Multigrid Solver based on Distributive Smoother and Residual Overweighting for Oseen Problems

L. Chen, X. Hu, M. Wang and J. Xu
Numer. Math. Theor. Meth. Appl.,  8(2),  237-252  (2015)

• Optimal Finite Element Methods for Interface Problems

J. Xu and S. Zhang
DD22 proceeding,  (2015)

• A Scalable Consistent Second-order SPH Solver for Unsteady Low Reynolds Number Flows

N. Trask, M. Maxey, K. Kim, M. Perego, M. L. Parks, K. Yang and J. Xu
Computer Methods in Applied Mechanics and Engineering,  289,  155-178  (2015)

• Well-posedness and Robust Preconditioners For Discretized Fluid-structure Interaction Systems

J. Xu and K. Yang
Comput. Methods Appl. Mech. Eng.,  292 69--91  (2015)

• Compositional Modeling of Reaction-Induced Injectivity Alteration During CO2 Flooding in Carbonate Reservoirs

C. Qiao, L. Li, R.T. Johns and J. Xu
SPE Annual Technical Conference and Exhibition,  Society of Petroleum Engineers  (2014)

• The Study on Hemodynamic Effect of Varied Support Models of BJUT-II VAD on Coronary Artery: A Primary CFD Study

Q. Zhang, B. Gao, K. Gu, Y. Chang and J. Xu
ASAIO Journal,  60(6) 643-651  (2014)

• Optimal Solvers for Fourth-Order PDEs Discretized on Unstructured Grids

S. Zhang and J. Xu
SIAM J. Numer. Anal.,  52(1),  282-307  (2014)

• Lower Bounds of the Discretization Error for Piecewise Polynomials

Q. Lin, H. Xie and J. Xu
Math. Comp. ,  83,  1-13  (2014)

• Full Eulerian Finite Element Method of a Phase Field Model for Fluid-structure Interaction Problem

P. Sun, J. Xu and L. X. Zhang
Computers & Fluids,  90,  1-8  (2014)

• Spatial Heterogeneity and Co-occurrence Patterns of Human Mucosal-associated Intestinal Microbiota

Z. Zhang, J. Geng, X. Tang, H. Fan, J. Xu, X. Wen, Z. Ma and P. Shi
ISME Journal,  8,  881-893  (2014)

• Numerical Study of Geometric Multigrid on CPU--GPU Heterogenous Computers

C. Feng, S. Shu, J. Xu and C. Zhang
Adv. Appl. Math. Mech.,  6,  1-23  (2014)

• A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem

B. Ayuso de Dios, F. Brezzi, L. D. Marini, J. Xu and L. Zikatanov
J. Sci. Comp.,  58(3),  517-547  (2014)

• An Auxiliary Space Preconditioner for the Black Oil Model and Its OpenMP Implemetation

C. Feng, S. Shu, and C.-S. Zhang
Domain Decomposition Methods in Science and Engineering XXI, Springer-Verlag Berlin Heidelberg,  129-140  (2013)

• Application of Auxiliary Space Preconditioning in Field-Scale Reservoir Simulation

X. Hu, J. Xu and C. Zhang
SCIENCE CHINA Mathematics,  56(12),  2737-2751  (2013)

• Multilevel Preconditioners for a New Generation Reservoir Simulator

Q. Li, J. Xu, X. Li, H. Li, S. Wu, B. Wang, and C. Zhang
SPE Reservoir Characterization and Simulation Conference and Exhibition,  SPE166011  (2013)

• The Single-Grid Multilevel Method and Its Applications

J. Xu
Inverse Probl. Imaging,  7(3),  987-1005  (2013)

• Combined Preconditioning with Applications in Reservoir Simulation

X. Hu, S. Wu, X.-H. Wu, J. Xu, C. Zhang, S. Zhang and L. Zikatanov
Multiscale Modeling and Simulation,  11(2),  507-521  (2013)

• On Adaptive Eulerian-Lagrangian Method for Linear Convection-Diffusion Problems

X. Hu, Y.-J. Lee, J. Xu and C. Zhang
J. Sci. Comput.,  58(1),  90-114  (2013)

• A Parallel Auxiliary Grid Algebraic Multigrid Method for Graphic Processing Units

L. Wang, X. Hu, J. Cohen and J. Xu
SIAM J. Sci. Comput.,  35(3),  C263-C283  (2013)

• Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid

X. Hu and P. S. Vassilevski and J. Xu
SIAM J. Numer. Anal.,  51(2),  1349-1369  (2013)

• Application of An Energy-minimizing Algebraic Multigrid Method for Subsurface Water Simulations

J.-R. C. Cheng, X.-H. Hai, S. Shu, J. Xu C. Zhang, S. Zhang and Z. Zhou
Int. J. Numer. Anal. Model.,  10(2),  374-388  (2013)

• Convergence and Optimality of the Adaptive Nonconforming Linear Element Method for the Stokes Problem

J. Hu and J. Xu
J. Sci. Comput.,  55(1),  125-148  (2013)

• Minimal Finite Element Spaces for 2m-th-order Partial Differential Equations in R^n

J. Xu and M. Wang
Math. Comp.,  82,  25-43  (2013)

• Two-grid Methods for Time-harmonic Maxwell Equations,

L. Zhong, S. Shu, J. Wang, and J. Xu
Numer. Linear Algebra Appl.,  20(1),  93-111  (2013)

• Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids

G. Yu, J. Xu and L. Zikatanov
Numer. Linear Algebra Appl. ,  20(5),  832-851  (2013)

• Local Multilevel Preconditioners for Elliptic Equations with Jump Coefficients on Bisection Grids

L. Chen, M. Holst, J. Xu and Y. Zhu
Comput. Vis. Sci.,  15(5),  271-289  (2012)

• A Discontinuous Galerkin Method for the Fourth-order Curl Problem

Q. Hong, J. Hu, S. Shu and J. Xu
J. Comput. Math.,  30(6),  565-578  (2012)

• Convergence of Numerical Analysis of V-cycle Multigrid Methods for Anisotropic Elliptic Equations

Y. Wu, L. Chen, X. Xie and J. Xu
IMA J. Numer. Anal.,  32(4),  1329-1347  (2012)

• Optimal Multilevel Methods for Graded Bisection Grids

L. Chen, R. H. Nochetto, and J. Xu
Numer. Math.,  120(1),  1-34  (2012)

• Fully Discrete Semi-Lagrangian Methods for Advection of Differential Forms

H. Heumann, R. Hiptmair, K. Li, and J. Xu
BIT.,  52(4),  981-1007  (2012)

• Convergence and Optimality of the Adaptive Morley Element Methods

J. Hu and Z.-C. Shi and J. Xu
Numer.Math.,  121(4),  731-752  (2012)

• Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations

L. Zhong, L. Chen, S. Shu, G. Wittum and J. Xu
Math. Comp.,  81,  623-642  (2012)

• Robust Preconditioner for H(curl) Interface Problems

J. Xu and Y. Zhu
Domain Decomposition Methods in Science and Engineering XIX,  173-180  (2011)

• Stable Finite Element Discretizations for Viscoelastic Flow Models

Y.-J. Lee and J. Xu and C.-S. Zhang
Handbook of Numerical Analysis,  16,  371-432  (2011)

• Global Existence, Uniqueness and Optimal Solvers of Discretized Viscoelastic Flow Models

Y.-J. Lee and J. Xu and C.-S. Zhang
Math Models and Methods in Applied Sciences,  21(8),  1713-1732  (2011)

• New Mixed Finite Elements for Plane Elasticity and Stokes Equations

X. Xie and J. Xu
China Math.,  54(7),  1499-1519  (2011)

• Development of a Fast Auxiliary Subspace Preconditioner for Numerical Reservoir Simulators

X. Hu, W. Liu, G. Qi, J. Xu, Y. Yan and C.-S. Zhang
SPE Reservoir Characterization and Simulation Conference,  SPE 148388  (2011)

• A Nonconforming Finite Element Method for Fourth Order Curl Equations in $\Bbb{R}^{3}$

B. Zheng and Q. Hu and J. Xu
Math. Comp.,  80,  1871--1886  (2011)

• Effects of Integrations and Adaptivity for the Eulerian--Lagrangian Method

J. Jia and X. Hu and J. Xu and C.-S. Zhang
J. Comp. Math.,  29,  367-395  (2011)

• New mixed finite elements for plane elasticity and Stokes equations

X. Xie and J. Xu
Sci. China Math.,  54(7),  1499-1519  (2011)

• Books of Peking University Modern Mathematics

with Gang Tian
Peking University Press,  2011

• Proceedings of the 20th International Conference on Domain Decomposition Methods

with R. Bank, M. Holst, and O. Widlund
Domain Decomposition Methods in Science and Engineering Series: Lecture Notes in Computational Science and Engineer 
San Diego,  Springer 2011

• Numerical Methods for Non-Newtonian Fluids

with R. Glowinski
Vol. 16 of Handbook of Numerical Analysis
Elsevier Publishing Services, 2011.

• A Eulerian-Lagrangian method for MHD equations

K. Li and C. Liu and J. Xu
(2011)

• A Combined Finite Element-Upwind Finite Volume Method for Liquid-Feed Direct Methanol Fuel Cell Simulations

P. Sun and C. Wang and J. Xu
Journal of Fuel Cell Science and Technology,  7(4),  doi:10.1115/1.4000630  (2010)

• Fast Poisson-Based Solvers for Linear and Nonlinear PDEs

J. Xu
Proceedings of the International Congress of mathematicians 2010 (ICM 2010) (2010)

• Numerical Studies of Adaptive Finite Element Methods for Two Dimensional Convection-Dominated Problems

P. Sun and L. Chen and J. Xu
J. Sci. Comput.,  43(1),  24-43  (2010)

• A Generalization of The Vertex-centered Finite Volume Scheme to Arbitrary High Order

A. Vogel and J. Xu and G. Wittum
Comput. Vis. Sci.  13,  221-228  (2010)

• Convergence of Adaptive Edge Finite Element Methods for ${\bf H}({\bf curl})$-elliptic Problems

L. Zhong and S. Shu and L. Chen and J. Xu
Numer. Linear Algebra Appl.  17  415--432  2010

• Phase Field Model of Thermo-induced Marangoni Effects in the Mixtures and Its Numerical Simulations with Mixed Finite Element Method

L. C. Sun, Pengtao, and J. Xu
Commun. Comput. Phys.  6  1095-1117  (2009)

• Numerical Solution to A Mixed Navier-Stokes/Darcy Model by the Two-grid Approach

M. Cai, M. Mu, and J. Xu
SIAM J. Numer. Anal.  47  3325--3338  (2009)

• Preconditioning Techniques for A Mixed Stokes/Darcy Model in Porous Media Applications

M. Cai, M. Mu, and J. Xu
J. Comput. Appl. Math.  233  346--355  (2009)

• Convergence and Optimality of Adaptive Mixed Finite Element Methods

L. Chen, M. Holst, and J. Xu
Math. Comp.  78  35--53  (2009)

• Preface: Special Issue on Adaptive and Multilevel Methods in Computational Electromagnetics

R. Hiptmair and J. Xu
J. Comput. Math.  27  561--562  (2009)

• New Numerical Techniques for A Three-dimensional Liquid-feed Direct Methanol Fuel Cell Model

P. Sun, G. Xue, and C. Wang and J. Xu
SIAM J. Appl. Math.  70  600--620  (2009)

• A domain decomposition method for a two-phase transport model in the cathode of a polymer electrolyte fuel cell

P. Sun, G. Xue, and C.-y. Wang and J. Xu
J. Comput. Phys.  228  6016--6036  (2009)

• Auxiliary Space Preconditoners for Mixed Finite Element Methods

R. S. Tuminaro, J. Xu, and Y. Zhu
Domian Decomposition Methods in Science and Engineering XVII. 70, 99-109 (2009)

• Optimal multilevel methods for $H({\rm grad})$, $H({\rm curl})$, and $H({\rm div})$ systems on graded and unstructured grids

J. Xu, L. Chen, and R. H. Nochetto
in "Multiscale, Nonlinear and Adaptive Approximation", Springer, 599-659, (2009)

• Analysis of linear and quadratic simplicial finite volume methods for elliptic equations

J. Xu and Q. Zou
Numer. Math.  111  469--492  (2009)

• Optimal algorithms for discretized partial differential equations

J. Xu
in "ICIAM 07 -- 6th International Congress on Industrial and Applied Mathematics", Eur. Math. Soc., Zurich, 409-444 (2009)

• Optimal error estimates for Nedelec edge elements for time-harmonic Maxwell's equations

L. Zhong, S. Shu, and G. Wittum and J. Xu
J. Comput. Math.  27  563--572  (2009)

• Fast numerical simulation of two-phase transport model in the cathode of a polymer electrolyte fuel cell

P. Sun, G. Xue, C. Wang, and J. Xu
Commun. Comput. Phys.      (2009)

• A Combined Finite Element-Upwind Finite Volume-Newton's Method for Liquid-Feed Direct Methanol Fuel Cell Simulations

P. Sun, G. Xue, C. Wang, and J. Xu
Proceedings of Sixth International Fuel Cell Science, Engineering and Technology Conference  (2008)

• Multilevel Preconditioning Methods for Discrete Models of Lattice Block Materials

S. Shu, I. Babuska, J. Xu, Y. Xiao, and L. Zikatanov
SIAM J. Sci. Comput. 31, 687-707  (2008)

• Auxiliary space preconditioning for edge elements

R. Hiptmair and J. Xu
IEEE Trans. Magnetics  44  938--941  (2008)

• Stability and accuracy of adapted finite element methods for singularly perturbed problems

L. Chen and J. Xu
Numer. Math.  109  167--191  (2008)

• New estimates for the rate of convergence of the method of subspace corrections

D. Cho, J. Xu, and L. Zikatanov
Numer. Math. Theory Methods Appl.  1  44?56  (2008)

• Convergence and optimal complexity of adaptive finite element eigenvalue computations

X. Dai, J. Xu, and A. Zhou
Numer. Math.  110  313--355  (2008)

• Local and parallel finite element algorithms for the Stokes problem

Y. He, J. Xu, A. Zhou, and J. Li
Numer. Math.  109  415--434  (2008)

• Superconvergence of quadratic finite elements on mildly structured grids

Y. Huang and J. Xu
Math. Comp.  77  1253--1268  (2008)

• A sharp convergence estimate for the method of subspace corrections for singular systems of equations

Y.-J. Lee, J. Wu, J. Xu, and L. Zikatanov
Math. Comp.  77  831--850  (2008)

• Convergence analysis on iterative methods for semidefinite systems

J. Wu, Y.-J. Lee, J. Xu, and L. Zikatanov
J. Comput. Math.  26  797--815  (2008)

• Uniformly-stable finite element methods for the Darcy-Stokes-Brinkman models

X. Xie, J. Xu, and G. Xue
J. Comput. Math.  26  437--455  (2008)

• Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients

J. Xu and Y. Zhu
Math. Models Methods Appl. Sci.  18  77?105  (2008)

• Optimal anisotropic simplicial meshes for minimizing interpolation errors in Lp-norm

L. Chen, P. Sun, and J. Xu
Mathematics of Computation  76  179?204  (2007)

• Superconvergent derivative recovery for Lagrange triangular elements of degree p on unstructured grids

R. E. Bank, J. Xu, and B. Zheng
SIAM J. Numer. Anal.  45  2032?2046 (electronic)  (2007)

• The finite element approximation of the nonlinear Poisson-Boltzmann equation

L. Chen, M. J. Holst, and J. Xu
SIAM J. Numer. Anal.  45  2298?2320  (2007)

• Nodal auxiliary space preconditioning in ${\bf H}({\bf curl})$ and ${\bf H}({\rm div})$ spaces

R. Hiptmair and J. Xu
SIAM J. Numer. Anal.  45  2483?2509 (electronic)  (2007)

• Robust subspace correction methods for nearly singular systems

Y.-J. Lee, J. Wu, J. Xu, and L. Zikatanov
Math. Models Methods Appl. Sci.  17  1937?1963  (2007)

• A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow

M. Mu and J. Xu
SIAM J. Numer. Anal.  45  1801?1813  (2007)

• A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem

P. Sun, R. D. Russell, and J. Xu
J. Comput. Phys.  224  1021--1048  (2007)

• A new class of Zienkiewicz-type non-conforming element in any dimensions

M. Wang, Z.-c. Shi, and J. Xu
Numer. Math.  106  335--347  (2007)

• Some $n$-rectangle nonconforming elements for fourth order elliptic equations

M. Wang, Z.-C. Shi, and J. Xu
J. Comput. Math.  25  408?420  (2007)

• Nonconforming tetrahedral finite elements for fourth order elliptic equations

M. Wang and J. Xu
Math. Comp.  76  1?18 (electronic)  (2006)

• An application of multigrid methods for a discrete elastic model for epitaxial systems

R. E. Caflisch, Y.-J. Lee, S. Shu, Y.-X. Xiao, and J. Xu
J. Comput. Phys.  219  697?714  (2006)

• Local and parallel finite element algorithms for the Navier-Stokes problem

Y. He, J. Xu, and A. Zhou
J. Comput. Math.  24  227?238  (2006)

• A two-grid discretization method for decoupling systems of partial differential equations

J. Jin and S. Shu and J. Xu
Math. Comp.  75  1617--1626 (electronic)  (2006)

• On the convergence of iterative methods for semidefinite linear systems

Y.-J. Lee, J. Wu, J. Xu, and L. Zikatanov
SIAM J. Matrix Anal. Appl.  28  634?641  (2006)

• New Formulations, Positivity Preserving Discretizations and Stability Analysis for Non-Newtonian Flow Models

Y.-J. Lee and J. Xu
Comput. Methods Appl. Mech. Engrg.  195  1180?1206  (2006)

• An algebraic multigrid method for higher-order finite element discretizations

S. Shu, D. Sun, and J. Xu
Computing  77  347--377  (2006)

• An algebraic multigrid method for finite element systems on criss-cross grids

S. Shu, J. Xu, Y. Yang, and H. Yu
Adv. Comput. Math.  25  287?304  (2006)

• A toy model for testing finite element methods to simulate extreme-mass-ratio binary systems

C. F. Sopuerta, P. Sun, P. Laguna, and J. Xu
Classical Quantum Gravity  23  251--285  (2006)

• The Morley element for fourth order elliptic equations in any dimensions

M. Wang and J. Xu
Numer. Math.  103  155?169  (2006)

• Modified Morley element method for a fourth elliptic singular perturbation problem

M. Wang, J. Xu, and Y. Hu
J. Comp. Math  24  113?120  (2006)

• On the well-posedness of a mathematical model for lithium-ion battery systems

J. Wu, J. Xu and H. Zou
Methods Appl. Anal.  13  275?297  (2006)

• Extending the applicability of multigrid methods

J. Brannick, M. Brezina, R. Falgout, T. Manteuffel, S. McCormick, J. Ruge, B. Sheehan, J. Xu, and L. Zikatanov
J. Phys.: Conf. Ser.  46  443?452  (2006)

• Partition of unity method on nonmatching grids for the Stokes problem

C. Bacuta, J. Chen, Y. Huang, J. Xu, and L. Zikatanov
J. Numer. Math.  13  157?169  (2005)

• Asymptotically Optimal and Linear-time Algorithm for Polygonal Curve Simplification

L. Chen, J. Z. Wang, and J. Xu
IEEE Transactions on Pattern Analysis and Machine Intelligence (2005)

• Measuring single cardiac myocyte contractile force via moving a magnetic bead

S. Yin, X. Zhang, C. Zhan, J. Wu, J. Cheung, and J. Xu
Biophysical Journal, 1489?1495  (2005)

• Multilevel homotopic adaptive finite element methods for convection dominated problems

L. Chen, P. Sun, and J. Xu
The Proceedings for 15th Conferences for Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering, 40  459?468  (2005)

• An optimal streamline diffusion finite element method for a singularly perturbed problem

L. Chen and J. Xu
Recent advances in adaptive computation, 383  191?201  (2005)

• Uniformly convergent multigrid methods for convection-diffusion problems without any constraint on coarse grids

H. Kim, J. Xu, and L. Zikatanov
Adv. Comput. Math.  20  385--399  (2004)

• Analysis of recovery type a posteriori error estimators for mildly structured grids

J. Xu and Z. Zhang
Math. Comp.  73  1139--1152 (electronic)  (2004)

• Optimal Delaunay triangulations

L. Chen and J. Xu
J. Comput. Math.  22  299-308  (2004)

• On an energy minimizing basis for algebraic multigrid methods

J. Xu and L. Zikatanov
Comput. Vis. Sci.  7  121--127  (2004)

• Regularity estimates for elliptic boundary value problems in Besov spaces

C. Bacuta, J. H. Bramble, and J. Xu
Math. Comp.  72  1577?1595 (electronic)  (2003)

• Regularity estimates for elliptic boundary value problems with smooth data on polygonal domains

C. Bacuta and J. H. Bramble and J. Xu
J. Numer. Math.  11  75--94  (2003)

• Asymptotically exact a posteriori error estimators. I. Grids with superconvergence

R. E. Bank and J. Xu
SIAM J. Numer. Anal.  41  2294?2312 (electronic)  (2003)

• Asymptotically exact a posteriori error estimators. II. General unstructured grids

R. E. Bank and J. Xu
SIAM J. Numer. Anal.  41  2313?2332 (electronic)  (2003)

• A conforming finite element method for overlapping and nonmatching grids

Y. Huang and J. Xu
Math. Comp.  72  1057?1066  (2003)

• A multigrid method based on graph matching for convection-diffusion equations

H. Kim, J. Xu, and L. Zikatanov
Numer. Linear Algebra Appl.  10  181--195  (2003)

• Successive subspace correction method for singular system of equations

Y.-J. Lee, J. Xu, and L. Zikatanov
Proceedings of the 14th International Conference on Domain Decomposition Method, 315--321  (2003)

• Some observations on Babuska and Brezzi theories

J. Xu and L. Zikatanov
Numer. Math.  94  195--202  (2003)

• Partition of Unity Method for Stokes Problem on Nonmatching Grids

C. Bacuta and J. Xu
Proceedings of the 2003 Copper Mountain Conference on Multigrid Methods (2003)

J. Wu and J. Xu
Proc Intl Symp Comp Applied PDEs, (2002)

• Algebraic multigrid method on lattice block materials

S. Shu, J. Xu, Y. Xiao, and L. Zikatanov
Recent Progress in Computational and Applied PDEs, 289 -307, (2002)

• Rate of convergence for parallel subspace correction methods for nonlinear variational inequalities

X.-C. Tai, B. Heimsund, and J. Xu
Proceedings of the 13rd International Conference on Domain Decomposition Method, 127--138  (2002)

• Newton-Krylov-multigrid algorithms for battery simulation

J. Wu, V. Srinivasan, J. Xu, and C. Wang
Journal of the Electrochemical Society  149  A1342  (2002)

• Local and parallel finite element algorithms for eigenvalue problems

J. Xu and A. Zhou
Acta Math. Appl. Sin. Engl. Ser.  18  185--200  (2002)

• Some multiscale methods for partial differential equations

J. Xu and A. Zhou
Contemmp. Math., 306  1--27  (2002)  

• The method of alternating projections and the method of subspace corrections in Hilbert space

J. Xu and L. Zikatanov
J. Amer. Math. Soc.  15  573--597  (2002)

• Global and uniform convergence of subspace correction methods for some convex optimization problems

X.-C. Tai and J. Xu
Math. Comp.  71  105--124  (2001)

• Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems

J. Xu and A. Zhou
Adv. Comput. Math.  14  293--327  (2001)

• Convergence of an explicit upwind finite element method to multi-dimensional conservation laws

J. Xu and L. Ying
J. Comput. Math.  19  87--100  (2001)

• The method of subspace corrections

J. Xu
J. Comput. Appl. Math.  128  335--362  (2000)

• A finite element multigrid preconditioner for Chebyshev-collocation method

J. Shen, F. Wang, and J. Xu
Appl. Numer. Math.  33  471--477  (2000)

• Local and parallel finite element algorithms based on two-grid discretizations

J. Xu and A. Zhou
Math. Comp.  69  881--909  (2000)

• A two-grid discretization scheme for eigenvalue problems

J. Xu and A. Zhou
Math. Comp.  70  17--25  (1999)

• A partition-of-unity finite element method for elliptic problems with highly oscillating coefficients

Y. Huang and J. Xu
In Proceedings for the Workshop on Scientific Computing, Hongkong99  27--30  (1999)

• On a Schur complement operator arisen from Navier-Stokes equations and its preconditioning

L. Shen and J. Xu
Advances in Comp Math Proceedings of the Guangzhou International Symposium edited by Zhongying Chen Yuesheng Li Charles a Micchelli and Yuesheng Xu,  202  481--490  (1998)

• Subspace correction methods for convex optimization problems

X.-C. Tai and J. Xu
Eleventh International Conference on Domain Decomposition Methods  130--139 (electronic)  (1998)

• A crosswind block iterative method for convection-dominated problems

F. Wang and J. Xu
SIAM J. Sci. Comput.  21  620--645 (electronic)  (1999)

• Some local and parallel properties of finite element discretizations

J. Xu and A. Zhou
Proceedings of the 11st International Conference on Domain Decomposition Method, 140--147 (electronic)  (1999)

• A monotone finite element scheme for convection-diffusion equations

J. Xu and L. Zikatanov
Math. Comp.  68  1429--1446  (1999)

• An agglomeration multigrid method for unstructured grids

T. F. Chan, J. Xu, and L. Zikatanov
Contemp. Math.,  218  67--81  (1998)

• A study of incorporating the multigrid method into the three-dimensional finite element discretization: a modular setting of grid generation and application

H. Cheng, G. Yeh, J. Xu, J. Cheng, and R. Carsel
Internat. J. Numer. Methods Engrg.  41  499--526  (1998)

• Some nonoverlapping domain decomposition methods

J. Xu and J. Zou
SIAM Rev.  40  857--914  (1998)

• The EAFE scheme and CWS method for Convection Dominated Problems

J. Xu
Proceedings of the 9th International Conference on Domain Decomposition Method (1997)

• Preconditioning the Poincar?-Steklov operator by using Greens function

J. Xu and S. Zhang
Math. Comp.  66  125--138  (1997)

• An Introdution to Multilevel Method

J. Xu
"Wavelets, Multilevel Methods and PDEs", (editors: Mark Ainsworth, Jeremy Levesley, Will Light, and Marco Marletta) Oxford University Press, New York      (1997)

• An Introdution to Multigrid Convergence Theory

J. Xu
Department of Mathematics, University of California, Los Angeles      (1996)

• An algorithm for coarsening unstructured meshes

R. E. Bank and J. Xu
Numer. Math.  73  1--36  (1996)

• The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids

J. Xu
Computing  56  215--235  (1996)

• Two-grid discretization techniques for linear and nonlinear PDEs

J. Xu
SIAM J. Numer. Anal.  33  1759--1777  (1996)

• A hierarchical basis multigrid method for unstructured grids

R. E. Bank and J. Xu
Fast Solvers for Flow Problems Proceedings of the Tenth GAMMSeminar Kiel 49  1--13  (1995)

• Error estimates on a new nonlinear Galerkin method based on two-grid finite elements

M. Marion and J. Xu
SIAM J. Numer. Anal.  32  1170--1184  (1995)

• The hierarchical basis multigrid method and incomplete LU decomposition

R. E. Bank and J. Xu
Contemp. math., 180  163--173  (1994)

• Some remarks on a multigrid preconditioner

J. Xu and J. Qin
SIAM J. Sci. Comput.  15  172--184  (1994)

• A novel two-grid method for semilinear elliptic equations

J. Xu
SIAM J. Sci. Comput.  15  231--237  (1994)

• Some two-grid finite element methods

J. Xu
Proceedings of the 6th International Conference on Domain Decomposition Method, 157  79--87  (1994)

• A New class of iterative methods for nonselfadjoint or indefinite problems

J. Xu
SIAM J. Numer. Anal.  29  303--319  (1992)

• A preconditioned GMRES method for nonsymmetric or indefinite problems

J. Xu and X.-C. Cai
Math. Comp.  59  311--319  (1992)

• Galerkin-wavelet methods for two-point boundary value problems

J. Xu and W. C. Shann
Numer. Math.  63  123--144  (1992)

• Iterative methods by space decomposition and subspace correction

J. Xu
SIAM Rev.  34  581--613  (1992)

• Iterative methods by SPD and small subspace solvers for nonsymmetric or indefinite problems

J. Xu
Proceedings of the 5th International Conference on Domain Decomposition Method, 106--118  (1992)

• A multilevel preconditioner for domain decomposition boundary systems

J. H. Bramble, J. E. Pasciak, and J. Xu
Proceedings of the Tenth International Conference on Computer Methods in Applied Science and Engineering (1992)

• Convergence estimates for multigrid algorithms without regularity assumptions

J. H. Bramble, J. E. Pasciak, J. P. Wang, and J. Xu
Math. Comp.  57  23--45  (1991)

• Convergence estimates for product iterative methods with applications to domain decomposition

J. H. Bramble, J. E. Pasciak, J. P. Wang, and J. Xu
Math. Comp.  57  1--21  (1991)

• The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms

J. H. Bramble, J. E. Pasciak, and J. Xu
Math. Comp.  56  1--34  (1991)

• Some estimates for a weighted $L^2$ projection

J. H. Bramble and J. Xu
Math. Comp.  56  463--476  (1991)

• Counterexamples concerning a weighted $L^2$ projection

J. Xu
Math. Comp.  57  563--568  (1991)

• Convergence estimates for some multigrid algorithms

J. Xu
Proceedings of the 3rd International Conference on Domain Decomposition Method, 174--187  (1990)

• Parallel multilevel preconditioners

J. H. Bramble, J. E. Pasciak, and J. Xu
Math. Comp.   174--187  (1990)

• Superconvergence of the gradient in piecewise linear finite-element approximation to a parabolic problem

V. Thom?e, J. Xu, and N. Y. Zhang
SIAM J. Numer. Anal.  26  553--573  (1989)

• A local post-processing technique for improving the accuracy in mixed finite-element approximations

J. H. Bramble and J. Xu
SIAM J. Numer. Anal.  26  1267--1275  (1988)

• The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

J. H. Bramble, J. E. Pasciak, and J. Xu
Math. Comp.  51  389--414  (1988)

• The analysis and improvement on infinite element algorithms

J. Xu and L. Ying
Chinese J. Numer. Math & Appl.  10  71-82  (1988)

• Analysis and improvement of algorithms for the infinite element method

J. Xu and L. A. Ying
Math. Numer. Sin.  8  164--174  (1986)

• Linear finite elements with high accuracy

Q. Lin and J. Xu
J. Comput. Math.  3  115--133  (1985)

• The error analysis and the improved algorithms for the infinite element method

J. Xu and Y. Long
Chinese J. Numer. Math. & Appl.  10, 71--82, (1988)

• Estimate of the Convergence Rate of the Finite element Solutions to Elliptic Equation of Second Order with Discontinuous Coefficients

J. Xu
Natur. Sci. J. Xiangtan Univ.  1  1-5  (1982)