Publications of Jie Shen

Books

  • Spectral Methods: Algorithms, Analysis and Applications (Springer Series in Computational Mathematics, V. 41) (by Jie Shen, Tao Tang and Li-Lian Wang, Springer, Aug. 2011), Erratum and the associated Matlab codes.
  • Spectral and High-Order Methods with Applications (by Jie Shen and Tao Tang, Science Press of China, 2006); Erratum and Matlab & Fortran codes for the book. You may purchase the book at www.amazon.com or at www.amazon.com.cn.


    Papers

    Disclaimer: The copyright for these papers belongs to the publisher of the journal. The papers may be downloaded for personal use only. Any other use requires prior permission of the author and the publisher.

    Current

    (with Yongyong Cai) Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field models for two-phase incompressible flows. To appear in Math. Comp.

    (with Zhiping Mao) Hermite spectral methods for fractional PDEs in unbounded domains. To appear in SIAM J. Sci. Comput.

    (with Qing Cheng and Xiaofeng Yang) Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. J. Comput. Phys. DOI. http://dx.doi.org/10.1016/j.jcp.2017.04.010

    (with Yongyong Cai, Jie Shen and Xiang Xu) A stable scheme and its convergence analysis for a 2D dynamic Q-tensor model of nematic liquid crystals. To appear in Math. Models Methods Appl. Sci.

    (with Zhijian Rong and Haijun Yu) A Nodal Sparse Grid Spectral Element Method for Multi-Dimensional Elliptic Partial Differential Equations. To appear in Inter. J. Numer. Anal. Model.

    (with Yongyong Cai and Heejun Choi) Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. To appear in Numer. Math.

    (with Lina Ma, Li-Lian Wang and Zhiguo Yang) Wavenumber explicit analysis of spectral-Galerkin methods for time-harmonic Maxwell equations in exterior domains. To appear in IMA J. Numer. Anal.

    (with Changtao Sheng) A hybrid spectral element method for fractional two-point boundary value problems. To appear in Numerical Mathematics: Theory, Methods and Applications.

    (with Haydar Alici) Highly accurate pseudospectral approximations of the prolate spheroidal wave equation for any bandwidth parameter and zonal wavenumber. J. Sci. Comput. 71:804-821, 2017.

    (with Sean Colbert-Kelly, G.B. McFadden and Daniel Phillips) Numerical Analysis and Simulation for a Generalized Planar Ginzburg-Landau Equation in a Circular Geometry. Comm. Math. Sci. 15:329-357, 2017.

    2016

    (with Yingwei Wang) Muntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems. SIAM J. Sci. Comput., 38:A2357-A2381, 2016.

    (with Zhiping Mao and Sheng Chen) Efficient and accurate spectral methods using general Jacobi functions for solving Riesz Fractional Differential Equations. Appl. Numer. Math., 106:165-181, 2016.

    (with Yingwei Wang and Jianlin Xia) Fast structured direct spectral methods for differential equations with variable coefficients. SIAM J. Sci. Comput., 38:A28-A54, 2016.

    (with M. Azaiez, F. Jelassi and M. Mint Brahim) Two Phases Stefan Problem with Smoothed Enthalpy. Comm. Math. Sci., 14:1625-1641, 2016.

    (with Tao Tang and Jiang Yang) On the maximum principle preserving schemes for the generalized Allen-Cahn Equation. Comm. Math. Sci. 14:1517-1534, 2016.

    (with Lina Hu and Lina Ma) Efficient Spectral-Galerkin Method and Analysis for Elliptic PDEs with Non-Local Boundary Conditions. J. Sci. Comput., 68:417-437, 2016.

    (with Yingwei Wang and Haijun Yu) Efficient spectral-element methods for electronic Schrodinger equation in one spatial dimension. To appear in Proceedings for the Sparse Grids and Applications 2016.

    (with Heejun Choi) Efficient splitting schemes for magneto-hydrodynamic equations. Science China Mathematics (English), 59:1495-1510, 2016.

    (with Changtao Sheng) A hybrid spectral element method for Volterra integral equations with weakly singular kernel. Science China Mathematics (Chinese), 46:1017-1036, 2016.

    (with Ying Chen) Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. J. Comput. Phys., 308:40-56, 2016.

    (with Ye Cao, C. A. Randall and Longqing Chen) Effect of multi-domain structure on ionic transport, electrostatics, and current evolution in BaTiO3 ferroelectric capacitor. Acta Materialia, 1112:224-230, 2016.

    (with Zhiping Mao) Efficient Spectral-Galerkin Methods for Fractional Partial Differential Equations with Variable Coefficients. J. Comput. Phys., 307:243-261, 2016.

    (with Sheng Chen and Li-Lian Wang) Generalized Jacobi functions and their applications to fractional differential equations. Math. Comp. 85:1603-1638, 2016.

    (with Jia Zhao, Xiaofeng Yang and Qi Wang) A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids. J. Comput. Phys. 305:539-556, 2016.

    2015

    (with Henk Dijkstra, Taylan Senqul and Shouhong Wang) Dynamic transitions of quasi-geostrophic channel flow. SIAM J. Appl. Math. 75:2361-2378, 2015.

    (with Changtao Sheng and Zhongqing Wang) Generalized Jacobi spectral-Galerkin method for nonlinear Volterra integral equations with weakly singular kernels. J. Math. Study., 48:315-329, 2015.

    (with Zhiping Mao) A semi-implicit spectral deferred correction method for two water wave models with nonlocal viscous term and numerical study of their decay rates. Science China Mathematics (in Chinese) 45:1153-1168, 2015.

    (with Jing An) Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem. Comput. Math. Appl. 69:1132-1143, 2015.

    (with S. Dong) A Pressure Correction Scheme for Generalized Form of Energy-Stable Open Boundary Conditions for Incompressible Flows. J. Comput. Phys. 291:254-278, 2015.

    (with Xiaofeng Yang) Decoupled energy stable schemes for phase-field models of two-phase incompressible flows. SIAM J. Numer. Anal. 53:279-296, 2015.

    (with Wei Li and Li-Shi Luo) Accurate solution and approximations of the linearized bgk equation for steady Couette flow. Computers & Fluids, 111:18-32, 2015.

    (with Lina Ma and Lil-Lian Wang) Spectral Approximation of Time-Harmonic Maxwell Equations in Three-dimensional Exterior Domains. Inter. J. Numer. Anal. Model. 12:366-383, 2015.

    (with Xiaofeng Yang an d Haijun Yu) Efficient energy stable numerical schemes for a phase-field moving contact line model. J. Comput. Phys. 284:617-630, 2015.

    (with Lina Hu, Claude-Michel Brauner and G.I. Sivashinsky) Modeling and Simulation of Fingering Pattern Formation In a Combustion Model. Math. Models & Methods Appl. Sci. 25:685-720, 2015.

    (with Fei Liu) Stabilized Semi-Implicit Spectral Deferred Correction Methods for Allen-Cahn and Cahn-Hilliard Equations. Math. Methods Appl. Sci., 38:4564-4575, 2015.

    (with Chun Liu and Xiaofeng Yang) Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density. J. Sci. Comput., 62:601-622, 2015.

    (with Taylan Senqul and Shouhong Wang) Pattern Formations of 2D Rayleigh-Benard Convection with No-Slip Boundary Conditions for the Velocity at the Critical Length Scales. Math. Methods Appl. Sci. 38:3792-3806, 2015.

    2014

    (with Ying He and Peijun Li) A New Spectral Method for Numerical Solution of the Unbounded Rough Surface Scattering Problem. J. Comput. Phys. 275:608-625, 2014.

    (with Ying He) Unconditionally Stable Pressure-Correction Schemes for a Linear Fluid-Structure Interaction Problem. Numer. Math.: Theory, Methods and Appl. 7:537-554, 2014.

    (with Ye Cao, C. A. Randall and Longqing Chen) Phase-field modeling of switchable diode-like current-voltage characteristics in ferroelectric BaTiO3. Appl. Phys. Lett., DOI: 104:182905, 2014.

    (with Ye Cao, C. A. Randall and Longqing Chen) Effect of ferroelectric polarization on ionic transport and resistance degradation in BaTiO3 by the phase-field approach. J. Am. Ceram. Soc., 97:3568-3575, 2014.

    (with Xiaofeng Yang) Decoupled energy stable schemes for phase-field models of two-phase complex fluids. SIAM J. Sci. Comput. 36:N122-B145, 2014.

    (with L. Chen, C. Xu and L. Luo) Parallel spectral-element direction splitting method for incompressible Navier-Stokes equations. Appl. Numer. Math. 84:66-79, 2014

    (with Jing An) Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction. J. Math. Study. 1:1-20, 2014.

    (with Li-Lian Wang and Haijun Yu) Approximations by Orthonormal Mapped Chebyshev Functions for Higher-Dimensional Problems In Unbounded Domains. J. Comput. Appl. Math. 265:264-275, 2014.

    2013

    (with Q. Wang and X. Yang) Mass and volume conservation in phase field models for binary fluids. Comm. Comput. Phys. 13:929-957, 2013

    (with Jing An) A Fourier-spectral-element method for transmission eigenvalue problems in radially stratified media. J. Sci. Comput. 57:670-688, 2013.

    (with Ye Cao, S. Bhattacharya, C. A. Randall and Longqing Chen) Role of polaron hopping in leakage current behavior of a SrTiO3 single crystal. J. Appl. Phys. V. 114, 224102, 2013.

    (with Jing An) An Efficient and Stable Spectral-Element Method for Acoustic Scattering by an Obstacle. East Asia J. Appl. Math. 3:190-208, 2013.

    (with F. Chen) A GPU Parallelized Spectral Method For Elliptic Equations. J. Comput. Phys. 250:555-564, 2013.

    (with Xiaofeng Yang, Greg Forest, Huiyuan Li, Chun Liu, Qi Wang and Falai Chen) Numerical Investigation of the Dynamics of drop formation and pitch-off using a phase-field model for two-phase complex fluids. J. Comput. Phys., 236:1-14, 2013.

    (with Z. Wang) Error analysis of the Strang time-splitting Laguerre-Hermite/Hermite collocation methods for The Gross-Pitaevskii equation. Foundation of Comput. Math., 13:99-137, 2013.

    (with F. Chen) Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn--Hilliard systems. Comm. Comput. Phys., 13:1189-1208, 2013.

    (with C. Collins and S. Wise) An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Comm. Comput. Phys., 13:929-957, 2013.

    2012

    (with S. Dong) A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible Flows with large density ratios. J. Comput. Phys., 231:5788-5804, 2012.

    (with F. Chen) Efficient spectral--Galerkin methods for systems of coupled-second-order equations and their applications. J. Comput. Phys., 231:5016-5028, 2012.

    (with Peijun Li) Analysis of the Scattering by an Unbounded Rough Surface. Math. Methods Appl. Sci., 35:2166-2184, 2012.

    (with Haijun Yu) On the approximation of the Fokker--Planck Equation of FENE dumbbell model, I: a new weighted formulation and an optimal spectral-Galerkin algorithm in 2-D. SIAM J. Numer. Anal. 50:1136-1161, 2012.

    (with Haijun Yu) Efficient Spectral Sparse Grid Methods and Applications to High Dimensional Elliptic Problems II Unbounded domains. SIAM J. Sci. Comput. 34:A1141-A1164, 2012.

    (with C. Wang, X. Wang and S. Wise) Second-order convex splitting schemes for gradient flows with Ehrlich-Schwoebel type energy: application to thin film epitaxy. SIAM J. Numer. Anal. 50:105-125, 2012.

    (with F. Chen and H. Yu) A new spectral element method for pricing European options under the Black-Scholes and Merton jump diffusion model. J. Sci. Comput., 52:499-518, 2012.

    (with Y. He and D. Nicholls) An efficient and stable spectral method for electromagnetic scattering from a layered periodic struture. J. Comput. Phys. 231:3007-3022, 2012.

    (with L. Chen and C. Xu) A unstructured nodal spectral-element method for the Navier-Stokes equations. Comm. Comput. Phys. 12:315-336, 2012.

    2011

    Modeling and numerical approximation of two-phase incompressible flows by a phase-field approach. Lecture Note Series, IMS, National University of Singapore, 2011.

    (with L. Chen and C. Xu) Spectral direction splitting schemes for the incompressible Navier-Stokes equations. East Asia J. Appl. Math., 1:215-234, (2011).

    (with X. Yang, G. Forest and C. Liu) Shear cell rupture of nematic liquid crystal droplets in viscous fluids. J. Non-Newtonian Fluid Mech. 166:487–499 (2011).

    (with Dinesh A. Shetty, Abhilash J. Chandy and Steven Frankel) A Pressure-Correction Scheme for rotational Navier-Stokes equations and its Application to Rotating Turbulent Flows. Commun. Comput. Phys., 9:740-755 (2011).

    (with L. Chen and C. Xu) A triangular spectral method for Stokes equations. Numer. Math.: Theory, Methods Appl., 4:158-179 (2011).

    2010

    (with Haijun Yu) Efficient Spectral Sparse Grid Methods and Applications to High Dimensional Elliptic Problems SIAM J. Sci. Comput., 32:3228-3250 (2010).

    (with Li-Lian Wang) Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. SIAM J. Numer. Anal., 48:1087-1109 (2010).

    (with S.C. Dong) An Unconditionally Stable Rotational Velocity-Correction Scheme for Incompressible Flows. J. Comp. Phys., 229:7013-7029 (2010).

    (with Xiaofeng Yang) Energy Stable Schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows. Chinese Ann. Math. series B, 31:743-758 (2010).

    (with Xiaofeng Yang) A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities. SIAM J. Sci. Comput., 32:1159-1179 (2010).

    (with Xiaofeng Yang) Numerical Approximations of Allen-Cahn and Cahn-Hilliard Equations. DCDS, Series A, 28:1669-1691 (2010).

    (with Y.Y. Kwan and J. Park) A mathematical and numerical study of incompressible flows with a surfactant monolayer. DCDS, Series A, 28:181-197 (2010).

    (with Huiyuan Li) Optimal Error Estimates in Jacobi-Weighted Sobolev Spaces For Polynomial Approximations on The Triangle. Math. Comp., 79:1621-1646 (2010).

    (with Qingqu Zhuang and Chuanju Xu) A coupled Legendre-Laguerre spectral-element method for the Navier-Stokes equations in unbounded domains. J. Sci. Comput., 42:1-22 (2010).

    (with J. Park and F. Chen) Modeling and simulation of switchings in ferroelectric liquid crystals. DCDS, Series A, 26:1419-1440 (2010).

    2009

    (with Qirong Fang and Li-Lian Wang) An Efficient and Accurate Spectral Method for Acoustic Scattering in Elliptic Domains. Numerical Mathematics: Theory, Methods and Application, 2:258-274 (2009).

    (with Weizhu Bao and Hailiang Li) A generalized Laguerre-Fourier-Hermite pseudospectral method for computing the dynamics of rotating in Bose-Einstein condensates. SIAM J. Sci. Comput., 31:3685-3711 (2009).

    (with E. A. Eliseev, A. N. Morozovska, S. V. Kalinin, Y. Li, M. D. Glinchuk, L. Chen and V. Gopalan) Surface effect on domain wall width in ferroelectrics. J. Appl. Physics, v. 106, 084102 (2009).

    (with David Nicholls) A Rigorous Numerical Analysis of the Transformed Field Expansion Method. SIAM J. Numer. Anal., 47:2708-2723 (2009).

    (with Xiaofeng Yang) An efficient moving mesh spectral method for the phase-field model of twophase flows. J. Comput. Phys., 228:2978-2992 (2009).

    (with Li-Lian Wang and Huiyuan Li) A triangular spectral element method using fully tensorial rational basis functions. SIAM J. Numer. Anal., 47:1619-1650 (2009).

    (with Dongbin Xiu) Efficient Stochastic Galerkin Methods For Random Diffusion Equations. J. Comput. Phys., 228:266-281, 2009.

    (with Li-Lian Wang) On Spectral Approximations In Elliptical Geometries Using Mathieu Functions. Math. Comp., 78:815-844, 2009.

    (with Li-Lian Wang) Some Recent Advances On Spectral Methods For Unbounded Domains. Commun. Comput. Phys., 5:195-241, 2009.

    2008

    (with Weizhu Bao) A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates. J. Comput. Phys. 227:9778-9793, 2008.
  • * Abstract * PDF file

    (with Mejdi Azaiez, Chuanju Xu and Qingqu Zhuang) Laguerre-Legendre spectral method for the Stokes problem in a semi-infinite channel. SIAM J. Numer. Anal., 47:271-292, 2008.
    * Abstract * PDF file

    (with Jin Ma and Yanhong Zhao) On Numerical Approximations of Forward-Backward Stochastic Differential Equations. SIAM J. Numer. Anal., 46:2636-2661, 2008.
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    (with Xiaofeng Yang, Zhenlu Cui, Greg Forest and Qi Wang) Dimensional Robustness & Instability of Sheared, Semi-Dilute, Nano-Rod Dispersions. Multi. Model. Simul. 7:622-654, (2008).
    * Abstract * PDF file

    (with J.L. Guermond and Xiaofeng Yang) Error analysis of fully discrete velocity-correction methods for incompressible flows. Math. Comp. 77:1387-1405 (2008).
    * Abstract * PDF file

    (with Benyu Guo and Li-Lian Wang) Generalized Jacobi Polynomials/Functions and their Applications. Appl. Numer. Math., DOI: 10.1016/j.apnum.2008.04.003 (2008).
    * Abstract * PDF file

    (With Jiahong Wu and Yuanming Yuan) A dual-Petrov-Galerkin method for the Kawahara-type equations. J. Sci. Comput. 34:48-63, 2008.
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    (with Benyu Guo) Irrational approximations and their applications to partial differential equations in exterior domains. Adv. Comput. Math. 28:237-267, 2008.
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    2007

    (with Chun Liu and Xiaofeng Yang) Dynamics of Defect Motion in Nematic Liquid Crystal Flow: Modeling and Numerical Simulation. Comm. Comput. Phys. 2:1184-1198, 2007.
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    (with Li-Lian Wang) Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains. SIAM J. Numer. Anal., 45:1954-1978, 2007.
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    (with Xiaofeng Yang) Error estimates for finite element approximations of consistent splitting schemes for incompressible flows. DCDS-B, 8:663-676, 2007.
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    (with C. Zhou, P. Yue, J Feng and Chun Liu) Heart-shaped bubbles rising in anisotropic liquids. Phys. of Fluids 19, 041703 (2007).
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    (With Yuen-Yick Kwan) An efficient direct parallel spectral-element solver for separable elliptic problems. J. Comput. Phys. 225:1721-1735, 2007.
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    (With Jiahong Wu and Yuanming Yuan) Eventual periodicity for the KdV equation on a half-line. Phys. D. 227:105-119, 2007.
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    (with Qirong Fang and D. Nicholls) A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. J. Comput. Phys. 224:1145-1169, 2007.
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    (with Li-Lian Wang) Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Appl. Numer. Math. 57:710-720, 2007.
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    (with Li-Lian Wang) Legendre and Chebyshev Dual-Petrov-Galerkin Methods for Hyperbolic equations. Int. J. Numer. Methods Eng. 196:3785-3797, 2007.
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    (with J. Pyo) Gauge-Uzawa methods for incompressible flows with variable density. J. Comput. Phys. 221:181-197 (2007)
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    (with O. Goubet) On the dual petrov-Galerkin formulation of the KDV equation on a finite interval. Adv. Diff. Eqn. 12:221-239 (2007)
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    (with Dongbin Xiu) An Efficient Spectral Method for Acoustic Scattering from Rough Surfaces. Commun. in Comput. Phys., 2:54-72 (2007)
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    2006

    (with J. L. Guermond and P. Minev) An Overview of Projection Methods for Incompressible Flows. Comput. Methods Appl. Mech. Eng. 195:6011-6045
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    (with David Nicholls) A Stable, High--Order Method for Two--Dimensional Bounded--Obstacle Scattering. SIAM J. Sci. Comput. 28:1398-1419 (2006)
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    (with Leszek Demkowicz) A few new (?) facts about the infinite elements. Comput. Methods Appl. Mech. Eng. 195:3572-3590 (2006)
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    (with Li-Lian Wang) Laguerre and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations. DCDS-B, 6:1381-1402 (2006)
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    (with R. Sani, O. Pironneau and P.M. Gresho) Pressure boundary condition for the time-dependent incompressible Navier-Stokes equations. Internat. J. Numer. Methods Fluids, 50:673-682 (2006)
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    (with Xiaofeng Yang, James J. Feng, Chun Liu) Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. J. Comput. Phys., 218:417-428 (2006)
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    (with Benyu Guo and Li-Lian Wang) Optimal spectral-Galerkin methods using generalized Jacobi polynomials. J. Sci. Comput. 27:305-322 (2006)
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    2005

    (with James J. Feng, Chun Liu, Pengtao Yue) An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. IMA Volumes in Mathematics and its Applications, 140:1--26, 2005.
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    (with Li-Lian Wang) Spectral Approximation of the Helmholtz equation with high wave numbers. SIAM J. Numer. Anal., 43:623-644, 2005.
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    (with Pengtao Yue, James J. Feng, Chun Liu) Transient Drop Deformation upon Startup of Shear in Viscoelastic Fluids. Phys. Fluids, 17:123101, 2005.
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    (with Pengtao Yue, James J. Feng, Chun Liu) Viscoelastic effects on drop deformation in steady shear. J. Fluid Mech., 540:427-437, 2005.
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    (with Weizhu Bao) A fourth-order time-splitting Laguerre-Hermite pseudo-spectral method for Bose-Einstein condensates. SIAM J. Sci. Comput., 26:2110-2028, 2005.
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    (with J. L. Guermond and P. Minev) Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions. SIAM J. Numer. Anal., 43:239-258, 2005.
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    (with Pengtao Yue, James J. Feng, Chun Liu) Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 129:163-176, 2005.
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    (with Pengtao Yue, James J. Feng, Chun Liu) Interfacial Forces and Marangoni Flow on a Nematic Drop Retracting in an Isotropic Fluid. J. Colloid Interface Sci., 290:281-288, 2005.
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    (with Li-Lian Wang) Error Analysis For Mapped Jacobi Spectral Methods. J. Sci. Comput., 24:183-218, 2005.
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    (with J.H. Pyo) Normal Mode Analysis of Second-Order Projection Methods for Incompressible Flows. Dis. Cont. Dyn. Sys. B, 5:817-840, 2005.
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    (with Benyu Guo and Chenglong Xu) Generalized Laguerre approximation and its applications to exterior problems. J. Comput. Math., 23:113-130, 2005.
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    2004

    (with Pengtao Yue, James J. Feng, Chun Liu) A Diffuse-Interface Method for Simulating Two-Phase Flows of Complex Fluids. J. Fluid Mech. 515:293-317, 2004.
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    (with J.M. Lopez and F. Marques) Complex dynamics in a short Taylor-Couette annulus with the top endwall stationary and the bottom rotating. J. Fluid Mech. 501:327-354, 2004.
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    (with J. L. Guermond) On the error estimates of rotational pressure-correction projection methods. Math. Comp. 73:1719-1737, 2004.
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    (with Li-Lian Wang) Error Analysis For Mapped Legendre Spectral And Pseudospectral Methods. SIAM J. Numer. Anal. 42:326-349, 2004.
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    2003

    (with J. L. Guermond) A New Class of Truly Consistent Splitting Schemes for Incompressible Flows. J. Comput. Phys., 192:262-276, 2003.
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    A New Dual-Petrov-Galerkin Method for Third and Higher Odd-order Differential Equations: Application to the KDV Equation. SIAM J. Numer. Anal., 41:1595-1619, 2003.
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    (with D. J. Seol, S. Y. Hu, Y. L. Li, L. Q. Chen and K. H. Oh) Three-dimensional phase-field modeling of spinodal decomposition in constrained films. Metals and Materials International, 9:61-66, 2003.
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    (with D. J. Seol, S. Y. Hu, Y. L. Li, L. Q. Chen and K. H. Oh) Computer simulation of spinodal decomposition in constrained films. Acta Materialia, 51:5173-5185, 2003.
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    (with J. L. Guermond) Velocity-correction projection methods for incompressible flows. SIAM J. Numer. Anal., 41:112-134, 2003.
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    (with Chun Liu) A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Physica D. 179:211-228, 2003.
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    (with Benyu Guo and Chenglong Xu) Spectral and pseudospectral approximations using Hermite functions: application to the DIrac equation. Adv. in Comp. Math., 19:35-55, 2003.
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    2002

    (with J.M. Lopez and F. Marques) An efficient spectral--projection method for the Navier-Stokes equations in cylindrical geometries II. Three dimensional cases, J. Comput. Phys. 176:384-401, 2002.
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    (with J. Lopez and F. Marques) Mode interactions in an enclosed swirling flow: A double Hopf between azimuthal wavenumbers 0 and 2, J. Fluid Mech., 455:263-281, 2002.
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    (with J.M. Lopez, J.E. Hart, F. Marques, S. Kittelman) Instability and mode interactions in a differentially-driven rotating cylinder, J. Fluid Mech., 462:383-409, 2002.
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    (with Benyu Guo and Zhongqing Wang) Chebyshev Rational Spectral and Pseudospectral Methods on a Semi-Infinite Interval. Inter. J. Numer. Methods Eng. 53:65-84, 2002.
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    2001

    (with Benyu Guo) On Spectral Approximations Using Modified Legendre Rational Functions: Application to Korteweg-de Vries Equation on the Half Line. Indina Math. J. 50:181-204, 2001.
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    (with Benyu Guo and Qiang Du) Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals, SIAM J. Numer. Anal. 39:735-762, 2001. (A Corrigendum for this paper is published in SIAM J. Numer. Anal., 41:796-798,2003)
    * Abstract * PDF file * PDF file for the Corrigendum

    (with J.M. Lopez and F. Marques) A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances, Phisica D, 156:81-97 2001.
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    (with Chun Liu) On liquid crystal flows with free-slip boundary conditions, Dis. Cont. Dyn. Sys., 7:307-318, 2001.
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    (with J. Zhu, L.Q. Chen and V. Tikare) Microstructure dependence of diffusional transport, Comput. Mat. Sci., v. 20, p. 37-47, 2001.
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    (with J. Zhu and L.Q. Chen) Morphological evolution during phase separation and coarsening with strong inhomogeneous elasticity, Modelling Simul. Mat. Sci. Eng., v. 9, p. 499-511, 2001.
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    (with J. Zhu, L.Q. Chen and V. Tikare) Computing the effective diffusivity using a spectral method, Mater. Sci. Eng. A, 311:135-141, 2001.
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    2000

    (with Benyu Guo and Zhongqing Wang) A rational approximation and its applications to differential equations on the half line. J. Sci. Comput. 15:117-147, 2000.
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    Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM J. Numer. Anal., 38:1113--1133, 2000.
    * Abstract * PDF file

    (with J.M. Lopez and F. Marques) Endwall effects in a periodically forced centrifugally unstable flow. Fluid Dynamics Research, vol. 27, p. 91-108, 2000.
    * Abstract * PDF file

    (with Benyu Guo) Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Numer. Math., 86:635--654, 2000.
    * Abstract * PDF file

    (with F. Wang and J. Xu) A finite element multigrid preconditioner for Chebyshev-collocation methods. Appl. Numer. Math., 33:471-477, 2000.
    * Abstract * PDF file

    A new fast Chebyshev-Fourier algorithm for Poisson-type equations in polar geometries. Appl. Numer. Math., 33:183-190, 2000.
    * Abstract * PDF file

    Before 2000

    (with S. Wang and T. Tachim Mejdo) On a wind-driven, double-gyre, quasi-geostrophic ocean model: numerical simulations and structural analysis. J. Comput. Phys., 155:387--409, 1999.
    * Abstract * PDF file

    Efficient spectral-Galerkin method IV. spherical geometries. SIAM J. Sci. Comput. V. 20, 1438-1455, 1999
    * Abstract * PDF file

    (with J. Zhu, L.Q. Chen and V. Tikare) Coarsening kinetics from a variable mobility Cahn-Hilliard equation - application of semi-implicit Fourier spectral method. Phys. Review E, v. 60, No. 4, p. 3564-3572, 1999.
    * Abstract * PDF file

    (with S. Wang) A fast and accurate numerical scheme for the primitive equations of the atmosphere. SIAM J. Numer. Anal. V. 36, 719-737, 1999
    * Abstract * PDF file

    (with J.M. Lopez) Numerical simulation of incompressible flows in cylindrical geometries using a spectral projection Method, Intern. J. Appl. Sci. & Comput. V. 5, 25--40, 1998.
    * Abstract * PDF file

    (with L.Q. Chen) Applications of semi-implicit Fourier-spectral method to phase field equations. Comput. Phys. Comm. v. 108, 147-158, 1998.
    * Abstract * PDF file

    (with J.M. Lopez) An efficient spectral--projection method for the Navier-Stokes equations in cylindrical geometries I. Axisymmetric cases, J. Comput. Phys. v. 139, p. 308-326, 1998
    * Abstract * * PDF file

    Efficient spectral-Galerkin method III. polar and cylindrical geometries, SIAM J. Sci. Comput. Vol. 18, 1583-1604, 1997
    * Abstract * PDF file

    (with R. Temam) Nonlinear Galerkin method using Legendre polynomials, in ``Studies in Advanced Mathematics'', vol. 3, 363--376, AMS and International Press, 1997.
    * Abstract * PDF file

    Pseudo-compressibility methods for the unsteady incompressible Navier-Stokes equations, in "Proceedings of the 1994 Beijing Symposium on Nonlinear Evolution Equations and Infinite Dynamical Systems", 68--78, Ed. Boling Guo, ZhongShan University Press, 1997.
    * Abstract * PDF file

    On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes, Math. Comp. vol. 65, 1039--1065, 1996.
    * Abstract * PDF file

    (with W.B. Liu) A new efficient spectral Galerkin method for singular perturbation problems, J. Sci. Comp. vol. 11, 411--437, 1996.
    * Abstract * PDF file

    Effcient Chebyshev-Legendre Galerkin methods for elliptic problems, Proceedings of ICOSAHOM'95, p. 233-239, Houston J. Math. 1996.
    * Abstract * PDF file

    On a new pseudo-compressibility method for the incompressible Navier-Stokes equations, Appl. Numer. Math. vol. 21, 71-90, 1996.
    * Abstract * PDF file

    On error estimates of the penalty method for the unsteady Navier-Stokes equations, SIAM J. Numer. Anal. Vol. 32, 386-403, 1995.
    * Abstract * PDF file

    (with R. Temam) Nonlinear Galerkin methods using Chebyshev and Legendre polynomials I. one dimensional case, SIAM J. Numer. Anal. Vol. 32, 215-234 (1995).
    * Abstract * PDF file

    On fast direct poisson solver, inf-sup constant and iterative Stokes solver by Legendre Galerkin method, J. Comput. Phys. Vol. 116, 184-188 (1995).
    * Abstract * PDF file

    Efficient spectral-Galerkin method II. Direct solvers for second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comput. vol. 16, 74-87 (1995).
    * Abstract * PDF file

    Efficient spectral-Galerkin method I. Direct solvers for second- and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput. vol. 15, 1489-1505 (1994).
    * Abstract * PDF file

    Remarks on pressure error estimates of the projection methods, Numer. Math. vol. 67, 513-520 (1994).
    * Abstract * PDF file

    A remark on the projection-3 method, Intern. J. Numer. Methods Fluids, 16, 249-253 (1993).
    * Abstract * PDF file

    On pressure stabilization method and projection methods for unsteady Navier-Stokes equations, Advances in Computer Methods for Partial Differential Equations-VII (eds. R. Vichnevestsky, D. Knight and G. Richter), 658-662, IMACS 1992.
    * Abstract * PDF file

    On error estimates of some higher-order projection and penalty-projection methods for the Navier-Stokes equations, Numer. Math., Vol. 62, 49-73 (1992)
    * Abstract * PDF file

    On error estimates of the projection methods for the Navier-Stokes equations: first-order schemes, SIAM J. Numer. Anal., Vol. 29, 55-77 (1992)
    * Abstract * PDF file

    Hopf bifurcation of the unsteady regularized driven cavity flow, J. Comp. Phys. Vol. 95, 228-245 (1991).
    * Abstract * PDF file

    Long time stability and convergence for fully discrete nonlinear Galerkin methods, Appl. Anal., 38, 201-229 (1990).
    * Abstract * PDF file

    Convergence of approximate attractors for a fully discrete system for reaction-diffusion equations, Numer. Func. Anal. Optim., 10, 1213-1234 (1989).
    * Abstract * PDF file

    A spectral-tau approximation for the Stokes and Navier-Stokes equations, Nath. Model. Num. Anal. 22:677-693 (1988).
    * Abstract * PDF file