A Bibliography of Publications of Jie Shen

Jie Shen Penn State University Mathematics Department

322 McAllister University Park, PA 16802

U.S.A.

Tel: +1 814 863 2036 FAX: +1 814 865 3735

E-mail: shen j@math.psu.edu (Internet)

25 November 2011 Version 1.04

Abstract

This bibliography records publications of Jie Shen.

Title word cross-reference

1988 [DHV89]. 1989 [CQ90]. 1992 [VKR92].

26-29 [CQ90]. 27-July [DHV89].

Advances [VKR92]. approximate [She89a]. approximation [She88b]. attractors [She89a].

bifurcation [She91]. Brunswick [VKR92].

case [ST95]. cavity [She89b]. Chebyshev [She95a]. Como [CQ90].

Computer [VKR92]. Conference [DHV89]. constant [She95c]. Convergence [She89a].

Differential [She90d]. diffusion [She89a]. dimensional [ST95]. Direct [She95a, She94a]. discrete [She89a]. discretization [She88a]. driven [She90b]. Dynamics [She89b].

Efficient [She94a]. Eleventh [DHV89]. equation [MRS89a]. equations [She88b]. Error [She92a]. Estimates [She92a]. existence [MRS89b].

fast [She95c]. First [She92a]. First-Order [She92a]. flow [She88a]. flows [ST89]. Fluid [DHV89]. fourth [She94a]. fourth-order [She94a]. fractional [ST89]. fully [She89a].

Galerkin [She90a]. held [DHV89]. high [She89b]. higher [She92b]. Hopf [She91].

ICOSAHOM’89 [CQ90]. II [She95a]. IMACS [VKR92]. incompressible [She88a]. inf [She95c]. inf-sup [She95c]. International [DHV89]. Italy [CQ90]. iterative [She95c].

Jersey [VKR92]. July [DHV89]. June [DHV89].

Legendre [She94a]. Leray [MRS89b]. Leray-Lions [MRS89b]. Lions [MRS89b]. Long [She90a].

method [She92c]. methods [She90a]. mixed [MRS89b].

Navier [She88b]. nonlinear [She90a]. numbers [She89b]. Numerical [She90b].

Olmo [CQ90]. one [ST95]. one-dimensional [ST95]. Order [She90d].

Partial [She90d]. penalty [She92b]. penalty-projection [She92b]. Poisson [She95c]. polynomials [She94a]. pressure [She92c]. Proceedings [DHV89]. Projection [She92a]. projection-3 [She93].

quasilinear [MRS89a].

reaction [She89a]. reaction-diffusion [She89a]. regularity [MRS89b]. Regularized [She89b]. remark [She93]. Remarks [She94b]. Reynolds [She89b].

scheme [She89a]. Schemes [She92a]. second [She94a]. second- [She94a]. seventh [VKR92]. simulation [She90b]. solutions [MRS89b]. solver [She95c]. solvers [She94a]. some [She92b]. spectral [She88b]. spectral-Galerkin [She94a]. spectral-tau [She88b]. stability [She90a]. stabilization [She92c]. stable [She90c]. Stokes [She88b]. sup [She95c]. Symposium [VKR92].

tau [She88b]. time [She88a].

type [MRS89b].

unconditionally [She90c].

unsteady [She90c]. USA [VKR92].

using [She94a].

VII [VKR92]. Villa [CQ90].

Virginia [DHV89].

Williamsburg [DHV89].

References

Canuto:1990:SHO

[CQ90] Claudio Canuto and Alfio Quarteroni, editors. Spectral and high order methods for partial differential equations: proceedings of the ICOSAHOM’89 Conference, Villa Olmo, Como, Italy, 26-29 June 1989. North-Holland, Amsterdam, The Netherlands, 1990. ISBN 0-444-88475-0. LCCN QA377 .I39 1989.

Dwoyer:1989:PEI

[DHV89] D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt, editors. Proceedings of the Eleventh International Conference on Numerical Methods in Fluid Dynamics, held in Williamsburg, Virginia, June 27-July 1, 1988, number 323 in Lecture Notes in Physics. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 1989. ISBN 0-387-51048-6 (New York), 3-540-51048-6 (Berlin). LCCN QA911 .I541 1988.

Michaux:1989:AQE

[MRS89a] B. Michaux, J. M. Rakotoson, and Jie Shen. On the approximation of a quasilinear equation. Math. Model. Num. Anal., 24(2):211–234, 1989.

Michaux:1989:ERS

[MRS89b] B. Michaux, J. M. Rakotoson, and Jie Shen. On the existence and regularity of solutions of a quasilinear mixed equation of leray-lions type. Acta Appl. Math., 12:287– 316, 1989.

Shen:1988:TDI

[She88a] Jie Shen. On time discretization of the incompressible flow. In Dwoyer et al. [DHV89], pages 538–542. ISBN 0-387-51048-6 (New York), 3-540-51048-6 (Berlin). LCCN QA911 .I541 1988.

Shen:1988:STA

[She88b] Jie Shen. A spectral-tau approximation for the Stokes and Navier– Stokes equations. Math. Model. Num. Anal., 22(4):677–693, 1988.

Shen:1989:CAA

[She89a] Jie Shen. Convergence of the approximate attractors for a fully discrete scheme for the reactiondiffusion equations. Numer. Func. Anal. Opt., 10(11-12):1213–1234,

Shen:1989:DRC

[She89b] Jie Shen. Dynamics of regularized cavity flow at high Reynolds numbers. Appl. Math. Let., 2(4):381– 384, 1989.

Shen:1990:LTS

[She90a] Jie Shen. Long time stability and convergence for fully discrete nonlinear Galerkin methods. Appl. Anal., 38:201–229, 1990.

Shen:1990:NSR

[She90b] Jie Shen. Numerical simulation of the regularized driven cavity flows at high Reynolds numbers. Comput. Meth. Appl. Mech. Engin., 80: 273–280, 1990.

Shen:1990:USS

[She90c] Jie Shen. On an unconditionally stable scheme for the unsteady Navier–Stokes equations. J. Comput. Math., 8(3):276–288, 1990.

Shen:1990:SHO

[She90d] Jie Shen. Spectral and high order methods for partial differential equations. In Canuto and Quarteroni [CQ90], page ?? ISBN 0-444-88475-0. LCCN QA377 .I39 1989.

Shen:1991:HBU

[She91] Jie Shen. Hopf bifurcation of the unsteady regularized driven cavity flows. J. Computational Physics, 95:228–245, 1991.

Shen:1992:EEP

[She92a] Jie Shen. On error estimates of projection methods for Navier–Stokes equations: First-order schemes. SIAM Journal on Numerical Analysis, 29(1):57–77, February 1992. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Shen:1992:EES

[She92b] Jie Shen. On error estimates of some higher order projection and penalty-projection schemes for the Navier–Stokes equations. Num. Math, 62:49–73, 1992.

Shen:1992:PSM

[She92c] Jie Shen. On pressure stabilization method and projection method for unsteady Navier–Stokes equations. In Vichnevetsky et al. [VKR92], pages 658–662.

Shen:1992:PSN

[She92d] Jie Shen. Projection schemes for the Navier–Stokes equations. Appl. Math. Let., 1992.

Shen:1993:RPM

[She93] Jie Shen. A remark on the projection-3 method. Int. J. Num. Meth. Fluids, 16:249–253, 1993.

Shen:1994:ESG

[She94a] Jie Shen. Efficient spectral-Galerkin method I. Direct solvers for second- and fourth-order equations by using Legendre polynomials. SIAM J. Scient. Stat. Comput., 15:1489–1505, 1994.

Shen:1994:RPE

[She94b] Jie Shen. Remarks on the pressure error estimates for the projection methods, 1994.

Shen:1995:ESG

[She95a] Jie Shen. Efficient spectral-Galerkin method II. direct solvers for second- and fourth-order equations by using Chebyshev polynomials. SIAM J. Scient. Stat. Comput., 16:74–87, 1995.

Shen:1995:EEP

[She95b] Jie Shen. On error estimates of the penalty method for unsteady Navier–Stokes equations. SIAM Journal on Numerical Analysis, 32 (2):386–403, April 1995. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Shen:1995:FPS

[She95c] Jie Shen. On fast Poisson solver, inf-sup constant and iterative Stokes solver by Legendre Galerkin method. J. Computational Physics, 116:184–188, 1995.

Shen:1989:NFS

[ST89] Jie Shen and R. Temam. A new fractional scheme for the approximation of incompressible flows. Mat. Aplic. Comput., 8(1):3–22, 1989.

Shen:1995:NGM

[ST95] Jie Shen and Roger Temam. Nonlinear Galerkin method using Chebyshev and Legendre polynomials. I. the one-dimensional case. SIAM Journal on Numerical Analysis, 32(1):215–234, February 1995. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Vichnevetsky:1992:ACM

[VKR92] R. Vichnevetsky, D. Knight, and G. Richter, editors. Advances in Computer Methods for Partial Differential Equations VII: Proceedings of the seventh IMACS International Symposium on Computer Methods for Partial Differential Equations, New Brunswick, New Jersey, USA, June 22–24, 1992. IMACS, Department of Computer Science, Rutgers University, New Brunswick, NJ, 1992. x + 860 pp.