Jie Shen
Publications listed in MathSciNet
| [1] | J. L. Guermond, P. Minev, and Jie Shen. An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Engrg., 195(44-47):6011-6045, 2006. |
| [2] | Jie Shen and Li-Lian Wang. Laguerre and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations. Discrete Contin. Dyn. Syst. Ser. B, 6(6):1381-1402 (electronic), 2006. |
| [3] | L. Demkowicz and Jie Shen. A few new (?) facts about infinite elements. Comput. Methods Appl. Mech. Engrg., 195(29-32):3572-3590, 2006. |
| [4] | R. L. Sani, J. Shen, O. Pironneau, and P. M. Gresho. Pressure boundary condition for the time-dependent incompressible Navier-Stokes equations. Internat. J. Numer. Methods Fluids, 50(6):673-682, 2006. |
| [5] | Li-Lian Wang and Jie Shen. Error analysis for mapped Jacobi spectral methods. J. Sci. Comput., 24(2):183-218, 2005. |
| [6] | Weizhu Bao and Jie Shen. A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. SIAM J. Sci. Comput., 26(6):2010-2028 (electronic), 2005. |
| [7] | James J. Feng, Chun Liu, Jie Shen, and Pengtao Yue. An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. In Modeling of soft matter, volume 141 of IMA Vol. Math. Appl., pages 1-26. Springer, New York, 2005. |
| [8] | Jie Shen and Li-Lian Wang. Spectral approximation of the Helmholtz equation with high wave numbers. SIAM J. Numer. Anal., 43(2):623-644 (electronic), 2005. |
| [9] | J. L. Guermond, P. Minev, and J. Shen. Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions. SIAM J. Numer. Anal., 43(1):239-258 (electronic), 2005. |
| [10] | Jae-Hong Pyo and Jie Shen. Normal mode analysis of second-order projection methods for incompressible flows. Discrete Contin. Dyn. Syst. Ser. B, 5(3):817-840, 2005. |
| [11] | Ben-yu Guo, Jie Shen, and Cheng-long Xu. Generalized Laguerre approximation and its applications to exterior problems. J. Comput. Math., 23(2):113-130, 2005. |
| [12] | J. M. Lopez, F. Marques, and J. Shen. Complex dynamics in a short annular container with rotating bottom and inner cylinder. J. Fluid Mech., 501:327-354, 2004. |
| [13] | J. L. Guermond and Jie Shen. On the error estimates for the rotational pressure-correction projection methods. Math. Comp., 73(248):1719-1737 (electronic), 2004. |
| [14] | Jie Shen and Li-Lian Wang. Error analysis for mapped Legendre spectral and pseudospectral methods. SIAM J. Numer. Anal., 42(1):326-349 (electronic), 2004. |
| [15] | J. L. Guermond and Jie Shen. A new class of truly consistent splitting schemes for incompressible flows. J. Comput. Phys., 192(1):262-276, 2003. |
| [16] | Jie Shen. A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: application to the KdV equation. SIAM J. Numer. Anal., 41(5):1595-1619 (electronic), 2003. |
| [17] | Qiang Du, Benyu Guo, and Jie Shen. Corrigendum: “Fourier spectral approximation to a dissipative system modeling the flow of liquid crystals [SIAM J.Numer.Anal. 39 (2001), no.3, 735-762 (electronic); MR1860443 (2002g:76006)]. SIAM J. Numer. Anal., 41(2):796-798 (electronic), 2003. |
| [18] | Ben-yu Guo, Jie Shen, and Cheng-long Xu. Spectral and pseudospectral approximations using Hermite functions: application to the Dirac equation. Adv. Comput. Math., 19(1-3):35-55, 2003. Challenges in computational mathematics (Pohang, 2001). |
| [19] | Chun Liu and Jie Shen. A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Phys. D, 179(3-4):211-228, 2003. |
| [20] | J. L. Guermond and Jie Shen. Velocity-correction projection methods for incompressible flows. SIAM J. Numer. Anal., 41(1):112-134 (electronic), 2003. |
| [21] | J. M. Lopez, J. E. Hart, F. Marques, S. Kittelman, and J. Shen. Instability and mode interactions in a differentially driven rotating cylinder. J. Fluid Mech., 462:383-409, 2002. |
| [22] | F. Marques, J. M. Lopez, and J. Shen. Mode interactions in an enclosed swirling flow: a double Hopf bifurcation between azimuthal wavenumbers 0 and 2. J. Fluid Mech., 455:263-281, 2002. |
| [23] | J. M. Lopez, F. Marques, and Jie Shen. An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. II. Three-dimensional cases. J. Comput. Phys., 176(2):384-401, 2002. |
| [24] | Ben-yu Guo, Jie Shen, and Zhong-qing Wang. Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval. Internat. J. Numer. Methods Engrg., 53(1):65-84, 2002. p and hp finite element methods: mathematics and engineering practice (St. Louis, MO, 2000). |
| [25] | Jean-Luc Guermond and Jie Shen. Quelques résultats nouveaux sur les méthodes de projection. C. R. Acad. Sci. Paris Sér. I Math., 333(12):1111-1116, 2001. |
| [26] | Qiang Du, Benyu Guo, and Jie Shen. Fourier spectral approximation to a dissipative system modeling the flow of liquid crystals. SIAM J. Numer. Anal., 39(3):735-762 (electronic), 2001. |
| [27] | Ben-Yu Guo and Jie Shen. On spectral approximations using modified Legendre rational functions: application to the Korteweg-de Vries equation on the half line. Indiana Univ. Math. J., 50(Special Issue):181-204, 2001. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000). |
| [28] | F. Marques, J. M. Lopez, and J. Shen. A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances. Phys. D, 156(1-2):81-97, 2001. |
| [29] | Chun Liu and Jie Shen. On liquid crystal flows with free-slip boundary conditions. Discrete Contin. Dynam. Systems, 7(2):307-318, 2001. |
| [30] | Ben-Yu Guo, Jie Shen, and Zhong-Qing Wang. A rational approximation and its applications to differential equations on the half line. J. Sci. Comput., 15(2):117-147, 2000. |
| [31] | Ben-Yu Guo and Jie Shen. Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. Numer. Math., 86(4):635-654, 2000. |
| [32] | Jie Shen. Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM J. Numer. Anal., 38(4):1113-1133 (electronic), 2000. |
| [33] | Jie Shen, Feng Wang, and Jinchao Xu. A finite element multigrid preconditioner for Chebyshev-collocation methods. In Proceedings of the Fourth International Conference on Spectral and High Order Methods (ICOSAHOM 1998) (Herzliya), volume 33, pages 471-477, 2000. |
| [34] | Jie Shen. A new fast Chebyshev-Fourier algorithm for Poisson-type equations in polar geometries. In Proceedings of the Fourth International Conference on Spectral and High Order Methods (ICOSAHOM 1998) (Herzliya), volume 33, pages 183-190, 2000. |
| [35] | J. M. Lopez, F. Marques, and J. Shen. Endwall effects in a periodically forced centrifugally unstable flow. Fluid Dynam. Res., 27(2):91-108, 2000. |
| [36] | Jie Shen, T. Tachim Medjo, and S. Wang. On a wind-driven, double-gyre, quasi-geostrophic ocean model: numerical simulations and structural analysis. J. Comput. Phys., 155(2):387-409, 1999. |
| [37] | Jie Shen. Efficient spectral-Galerkin methods. IV. Spherical geometries. SIAM J. Sci. Comput., 20(4):1438-1455 (electronic), 1999. |
| [38] | Jie Shen and Shouhong Wang. A fast and accurate numerical scheme for the primitive equations of the atmosphere. SIAM J. Numer. Anal., 36(3):719-737 (electronic), 1999. |
| [39] | J. M. Lopez and Jie Shen. Numerical simulation of incompressible flows in cylindrical geometries using a spectral projection method. Internat. J. Appl. Sci. Comput., 5(1):25-40, 1998. |
| [40] | J. M. Lopez and Jie Shen. An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. I. Axisymmetric cases. J. Comput. Phys., 139(2):308-326, 1998. |
| [41] | Jie Shen. Efficient spectral-Galerkin methods. III. Polar and cylindrical geometries. SIAM J. Sci. Comput., 18(6):1583-1604, 1997. |
| [42] | Jie Shen and Roger Temam. Nonlinear Galerkin method using Legendre polynomials. In Nonlinear evolutionary partial differential equations (Beijing, 1993), volume 3 of AMS/IP Stud. Adv. Math., pages 363-376. Amer. Math. Soc., Providence, RI, 1997. |
| [43] | W. B. Liu and Jie Shen. A new efficient spectral Galerkin method for singular perturbation problems. J. Sci. Comput., 11(4):411-437, 1996. |
| [44] | Jie Shen. On a new pseudocompressibility method for the incompressible Navier-Stokes equations. Appl. Numer. Math., 21(1):71-90, 1996. |
| [45] | Jie Shen. On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes. Math. Comp., 65(215):1039-1065, 1996. |
| [46] | Jie Shen. On error estimates of the penalty method for unsteady Navier-Stokes equations. SIAM J. Numer. Anal., 32(2):386-403, 1995. |
| [47] | Jie Shen. On fast direct Poisson solver, inf-sup constant and iterative Stokes solver by Legendre-Galerkin method. J. Comput. Phys., 116(1):184-188, 1995. |
| [48] | Jie Shen and Roger Temam. Nonlinear Galerkin method using Chebyshev and Legendre polynomials. I. The one-dimensional case. SIAM J. Numer. Anal., 32(1):215-234, 1995. |
| [49] | Jie Shen. Efficient spectral-Galerkin method. II. Direct solvers of second- and fourth-order equations using Chebyshev polynomials. SIAM J. Sci. Comput., 16(1):74-87, 1995. |
| [50] | Jie Shen. Efficient spectral Galerkin methods for some elliptic problems. In Mathematics of Computation 1943-1993: a half-century of computational mathematics (Vancouver, BC, 1993), volume 48 of Proc. Sympos. Appl. Math., pages 373-376. Amer. Math. Soc., Providence, RI, 1994. |
| [51] | Jie Shen. Efficient spectral-Galerkin method. I. Direct solvers of second- and fourth-order equations using Legendre polynomials. SIAM J. Sci. Comput., 15(6):1489-1505, 1994. |
| [52] | Jie Shen. Remarks on the pressure error estimates for the projection methods. Numer. Math., 67(4):513-520, 1994. |
| [53] | Jie Shen. A remark on the projection-3 method. Internat. J. Numer. Methods Fluids, 16(3):249-253, 1993. |
| [54] | Jie Shen. On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations. Numer. Math., 62(1):49-73, 1992. |
| [55] | Jie Shen. On error estimates of projection methods for Navier-Stokes equations: first-order schemes. SIAM J. Numer. Anal., 29(1):57-77, 1992. |
| [56] | Jie Shen. Projection methods for time-dependent Navier-Stokes equations. Appl. Math. Lett., 5(1):35-37, 1992. |
| [57] | Jie Shen. On an unconditionally stable scheme for the unsteady Navier-Stokes equations. J. Comput. Math., 8(3):276-288, 1990. |
| [58] | Jie Shen. Numerical simulation of the regularized driven cavity flows at high Reynolds numbers. In Spectral and high order methods for partial differential equations (Como, 1989), pages 273-280. North-Holland, Amsterdam, 1990. |
| [59] | Jie Shen. Long time stability and convergence for fully discrete nonlinear Galerkin methods. Appl. Anal., 38(4):201-229, 1990. |
| [60] | B. Michaux, J.-M. Rakotoson, and J. Shen. On the approximation of a quasilinear mixed problem. RAIRO Modél. Math. Anal. Numér., 24(2):211-234, 1990. |
| [61] | J. Shen and R. Temam. A new fractional scheme for the approximation of incompressible flows. Mat. Apl. Comput., 8(1):3-22, 1989. |
| [62] | Jie Shen. Convergence of approximate attractors for a fully discrete system for reaction-diffusion equations. Numer. Funct. Anal. Optim., 10(11-12):1213-1234 (1990), 1989. |
| [63] | Jie Shen. Dynamics of regularized cavity flow at high Reynolds numbers. Appl. Math. Lett., 2(4):381-384, 1989. |
| [64] | Jie Shen. A spectral-tau approximation for the Stokes and Navier-Stokes equations. RAIRO Modél. Math. Anal. Numér., 22(4):677-693, 1988. |
| [65] | B. Michaux, J.-M. Rakotoson, and J. Shen. On the existence and regularity of solutions of a quasilinear mixed equation of Leray-Lions type. Acta Appl. Math., 12(3):287-316, 1988. |