Publications of Jie Shen

Books

  • New book: 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

    Here is a MathSciNet list of my publications. PDF files for most of my publications are available online below. Please e-mail me if you would like to have papers which are not available here.

    Current

    (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., DOI 10.1007/s10208-012-9124-x, June 2012.

    (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 F. Liu) Stabilized Semi-Implicit Spectral Deferred Correction Methods for Allen-Cahn and Cahn-Hilliard Equations. To appear in Math. Methods Appl. Sci.

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

    (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 Q. Wang and X. Yang) Mass-conserved phase field models for binary fluids. To appear in Comm. Comput. Phys.

    (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, S. Wang and X. Wang) 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) A 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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (with Benyu Guo) Irrational approximations and their applications to partial differential equations in exterior domains. Adv. Comput. Math. 28:237-267, 2008.
    * Abstract * PDF file

    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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (with Xiaofeng Yang) Error estimates for finite element approximations of consistent splitting schemes for incompressible flows. DCDS-B, 8:663-676, 2007.
    * Abstract * PDF file

    (with C. Zhou, P. Yue, J Feng and Chun Liu) Heart-shaped bubbles rising in anisotropic liquids. Phys. of Fluids 19, 041703 (2007).
    * Abstract * PDF file

    (With Yuen-Yick Kwan) An efficient direct parallel spectral-element solver for separable elliptic problems. J. Comput. Phys. 225:1721-1735, 2007.
    * Abstract * PDF file

    (With Jiahong Wu and Yuanming Yuan) Eventual periodicity for the KdV equation on a half-line. Phys. D. 227:105-119, 2007.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (with Li-Lian Wang) Fourierization of the Legendre-Galerkin method and a new space-time spectral method. Appl. Numer. Math. 57:710-720, 2007.
    * Abstract * PDF file

    (with Li-Lian Wang) Legendre and Chebyshev Dual-Petrov-Galerkin Methods for Hyperbolic equations. Int. J. Numer. Methods Eng. 196:3785-3797, 2007.
    * Abstract * PDF file

    (with J. Pyo) Gauge-Uzawa methods for incompressible flows with variable density. J. Comput. Phys. 221:181-197 (2007)
    * Abstract * PDF file

    (with O. Goubet) On the dual petrov-Galerkin formulation of the KDV equation on a finite interval. Adv. Diff. Eqn. 12:221-239 (2007)
    * Abstract * PDF file

    (with Dongbin Xiu) An Efficient Spectral Method for Acoustic Scattering from Rough Surfaces. Commun. in Comput. Phys., 2:54-72 (2007)
    * Abstract * PDF file

    2006

    (with J. L. Guermond and P. Minev) An Overview of Projection Methods for Incompressible Flows. Comput. Methods Appl. Mech. Eng. 195:6011-6045
    * Abstract * PDF file

    (with David Nicholls) A Stable, High--Order Method for Two--Dimensional Bounded--Obstacle Scattering. SIAM J. Sci. Comput. 28:1398-1419 (2006)
    * Abstract * PDF file

    (with Leszek Demkowicz) A few new (?) facts about the infinite elements. Comput. Methods Appl. Mech. Eng. 195:3572-3590 (2006)
    * Abstract * PDF file

    (with Li-Lian Wang) Laguerre and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations. DCDS-B, 6:1381-1402 (2006)
    * Abstract * PDF file

    (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)
    * Abstract * PDF file

    (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)
    * Abstract * PDF file

    (with Benyu Guo and Li-Lian Wang) Optimal spectral-Galerkin methods using generalized Jacobi polynomials. J. Sci. Comput. 27:305-322 (2006)
    * Abstract * PDF file

    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.
    * Abstract * PDF file

    (with Li-Lian Wang) Spectral Approximation of the Helmholtz equation with high wave numbers. SIAM J. Numer. Anal., 43:623-644, 2005.
    * Abstract * PDF file

    (with Pengtao Yue, James J. Feng, Chun Liu) Transient Drop Deformation upon Startup of Shear in Viscoelastic Fluids. Phys. Fluids, 17:123101, 2005.
    * Abstract * PDF file

    (with Pengtao Yue, James J. Feng, Chun Liu) Viscoelastic effects on drop deformation in steady shear. J. Fluid Mech., 540:427-437, 2005.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (with Li-Lian Wang) Error Analysis For Mapped Jacobi Spectral Methods. J. Sci. Comput., 24:183-218, 2005.
    * Abstract * PDF file

    (with J.H. Pyo) Normal Mode Analysis of Second-Order Projection Methods for Incompressible Flows. Dis. Cont. Dyn. Sys. B, 5:817-840, 2005.
    * Abstract * PDF file

    (with Benyu Guo and Chenglong Xu) Generalized Laguerre approximation and its applications to exterior problems. J. Comput. Math., 23:113-130, 2005.
    * Abstract * PDF file

    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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (with J. L. Guermond) On the error estimates of rotational pressure-correction projection methods. Math. Comp. 73:1719-1737, 2004.
    * Abstract * PDF file

    (with Li-Lian Wang) Error Analysis For Mapped Legendre Spectral And Pseudospectral Methods. SIAM J. Numer. Anal. 42:326-349, 2004.
    * Abstract * PDF file

    2003

    (with J. L. Guermond) A New Class of Truly Consistent Splitting Schemes for Incompressible Flows. J. Comput. Phys., 192:262-276, 2003.
    * Abstract * PDF file

    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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (with J. L. Guermond) Velocity-correction projection methods for incompressible flows. SIAM J. Numer. Anal., 41:112-134, 2003.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (with Chun Liu) On liquid crystal flows with free-slip boundary conditions, Dis. Cont. Dyn. Sys., 7:307-318, 2001.
    * Abstract * PDF file

    (with J. Zhu, L.Q. Chen and V. Tikare) Microstructure dependence of diffusional transport, Comput. Mat. Sci., v. 20, p. 37-47, 2001.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    (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.
    * Abstract * PDF file

    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.
    * Abstract * PDF file

    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

    1990-1999

    (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