Online Publications of Jie Shen

Here is a MathSciNet list of my publications and their BIBTEX entries (license to MathSciNet is required). PDF and/or PostScript files for some of my recent publications are available online below. Please e-mail me if you would like to have papers which are not available here.

Current

(with Li-Lian Wang) ON Spectral Approximations In Elliptical Geometries Using Mathieu Functions. To appear in Math. Comp.

(with Li-Lian Wang) Some Recent Advances On Spectral Methods For Unbounded Domains. To appear in Commun. Comput. Phys.

(with Mejdi Azaiez, Chuanju Xu and Qingqu Zhuang) A Laguerre-Legendre spectral method for the Stokes problem in a semi-infinite channel. To appear in SIAM J. Numer. Anal.

(with Jin Ma and Yanhong Zhao) On Numerical Approximations of Forward-Backward Stochastic Differential Equations. To appear in SIAM J. Numer. Anal.

(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).

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

(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).

(with Chun Liu and Xiaofeng Yang) Dynamics of Defect Motion in Nematic Liquid Crystal Flow: Modeling and Numerical Simulation. To appear in Comm. Comput. Phys.

(With Jiahong Wu and Yuanming Yuan) A dual-Petrov-Galerkin method for the Kawahara-type equations. To appear in J. Sci. Comput.

2007

(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.

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

(with C. Zhou, P. Yue, J Feng and Chun Liu) Heart-shaped bubbles rising in anisotropic liquids. Phys. of Fluids 19, 041703 (2007); DOI:10.1063/1.2722421.

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

(With Jiahong Wu and Yuanming Yuan) Eventual periodicity for the KdV equation on a half-line. Phys. D. DOI: 10.1016/physd.2007.02.003.

(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.

(with Benyu Guo) Irrational approximations and their applications to partial differential equations in exterior domains. Adv. Comput. Math. DOI 10.1007/s10444-006-9020-5.

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

(with Li-Lian Wang) Legendre and Chebyshev Dual-Petrov-Galerkin Methods for Hyperbolic equations. Int. J. Numer. Methods Eng. DOI:10.1016/j.cma.2006.10.031.

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

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

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

2006

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

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

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

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

(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)

(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)

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

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.

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

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

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

(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.

(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.

(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.

(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.

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

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

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

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.

(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.

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

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

2003

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

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.

(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.

(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.

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

(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.

(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.

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.

(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.

(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.

(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.

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.

(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)

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.

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

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

(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.

(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.

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.

Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM J. Numer. Anal., 38:1113--1133, 2000.

(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.

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

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

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

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.

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

(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.

(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

(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.

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

(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

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

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

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.

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

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

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

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

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

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

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

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).

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).

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

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

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.

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

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

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

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

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

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