• Papers

• Two-grid methods for time-harmonic Maxwell equations

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

• Convergence and Optimality of the Adaptive Morley Element Methods

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

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

J. Xu and M. Wang
Math. Comp., 82, 281 25–43 (2012)

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

G.Yu,  J. Xu, and L. Zikatanov
Numer. Linear Algebra Appl., 2012 (to appear).

• 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)

• Stable Finite Element Discretizations for Viscoelastic Flow Models

Handb. of Numer. Anal.  16  371-433  (2011)

• Global existence, uniqueness and optimal solvers of discretized viscoelastic flow models

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

• New mixed finite elements for plane elasticity and Stokes equations

X. Xie and J. Xu
Science China Math., Vol. 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, Q. Hu and J. Xu
Math. Comp.  80,  1871–1886  (2011)

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

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

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

P. Sun, C. Wang, and J. Xu
J. Fuel Cell Sci. Tech.  7  14  (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, L. Chen, and J. Xu
J. Sci. Comput.  43  24--43  (2010)

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

A. Vogel, 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, 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

W. Ming 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 Poincaré-Steklov operator by using Green's function

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

• 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. Thomée, 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)

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