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## Gottlieb, David I.

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 Author ID: gottlieb.david-i Published as: Gottlieb, D.; Gottlieb, David; Gottlieb, David I. External Links: MGP · Wikidata · GND
 Documents Indexed: 122 Publications since 1970, including 4 Books Biographic References: 2 Publications
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#### Co-Authors

 0 single-authored 21 Abarbanel, Saul S. 14 Turkel, Eli L. 13 Hesthaven, Jan S. 13 Shu, Chi-Wang 8 Breuer, Shlomo 8 Don, Wai Sun 8 Lustman, Liviu 7 Tadmor, Eitan 5 Orszag, Steven Alan 4 Temam, Roger Meyer 3 Cai, Wei 3 Gottlieb, Sigal 2 Chen, Qianyong 2 Costa, Bruno T. 2 Dettori, Lucia 2 Gunzburger, Max D. 2 Hussaini, M. Yousuff 2 Jung, Jae-Hun 2 Solomonoff, Alex 2 Streett, Craig L. 1 Abarbanel, A. 1 Carpenter, Mark H. 1 Chertock, Alina E. 1 Duth, Pravir 1 Dwoyer, Douglas L. 1 Gelb, Anne 1 Harten, Ami 1 Jameson, Leland M. 1 Karniadakis, George Em 1 Rudy, David H. 1 Salas, Manuel D. 1 Schilling, Oleg 1 Sendersky, R. 1 Townsend, James C. 1 Vandeven, Hervé 1 Voigt, Robert G. 1 Yang, Buyun
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#### Serials

 13 Journal of Computational Physics 9 SIAM Journal on Numerical Analysis 9 Journal of Scientific Computing 7 Mathematics of Computation 5 Applied Numerical Mathematics 4 Journal of Mathematical Analysis and Applications 3 Computer Methods in Applied Mechanics and Engineering 2 Computers and Fluids 2 Computers & Mathematics with Applications 2 Journal of Computational and Applied Mathematics 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Scientific and Statistical Computing 2 Linear Algebra and its Applications 2 SIAM Journal on Scientific Computing 2 Communications in Computational Physics 1 Journal of Fluid Mechanics 1 Annales Polonici Mathematici 1 Numerische Mathematik 1 Quarterly of Applied Mathematics 1 Studies in Applied Mathematics 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Comptes Rendus. Mécanique. Académie des Sciences, Paris 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Cambridge Monographs on Applied and Computational Mathematics
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#### Fields

 56 Numerical analysis (65-XX) 43 Partial differential equations (35-XX) 30 Fluid mechanics (76-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 6 Optics, electromagnetic theory (78-XX) 5 Special functions (33-XX) 5 Ordinary differential equations (34-XX) 3 General and overarching topics; collections (00-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH

108 Publications have been cited 3,789 times in 2,530 Documents Cited by Year
Numerical analysis of spectral methods: Theory and applications. Zbl 0412.65058
Gottlieb, David; Orszag, Steven A.
1977
Spectral methods for time-dependent problems. Zbl 1111.65093
Hesthaven, Jan S.; Gottlieb, Sigal; Gottlieb, David
2007
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. Zbl 0832.65098
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
1994
On the Gibbs phenomenon and its resolution. Zbl 0885.42003
Gottlieb, David; Shu, Chi-Wang
1997
A stable and conservative interface treatment of arbitrary spatial accuracy. Zbl 0921.65059
Carpenter, Mark H.; Nordström, Jan; Gottlieb, David
1999
The stability of numerical boundary treatments for compact high-order finite-difference schemes. Zbl 0791.76052
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
1993
Spectral methods for hyperbolic problems. Zbl 0974.65093
Gottlieb, D.; Hesthaven, J. S.
2001
Theory and applications of spectral methods. Zbl 0599.65079
Gottlieb, David; Hussaini, M. Yousuff; Orszag, Steven A.
1984
Spectral computations of one dimensional inviscid compressible flows. Zbl 0561.76076
Gottlieb, D.; Lustman, L.; Orszag, S. A.
1981
A mathematical analysis of the PML method. Zbl 0887.65122
Abarbanel, Saul; Gottlieb, David
1997
On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function. Zbl 0781.42022
Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Hervé
1992
The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A study of the boundary error. Zbl 0839.65098
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun
1995
Spectral methods on arbitrary grids. Zbl 0862.65054
Carpenter, Mark H.; Gottlieb, David
1996
A stable penalty method for the compressible Navier-Stokes equations. I: Open boundary conditions. Zbl 0853.76061
Hesthaven, J. S.; Gottlieb, D.
1996
The spectrum of the Chebyshev collocation operator for the heat equation. Zbl 0537.65085
Gottlieb, David; Lustman, Liviu
1983
Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives. Zbl 0467.76062
Abarbanel, Saul; Gottlieb, David
1981
A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations. Zbl 0699.65079
Funaro, D.; Gottlieb, D.
1988
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes. Zbl 1123.65097
Kanevsky, Alex; Carpenter, Mark H.; Gottlieb, David; Hesthaven, Jan S.
2007
Well-posed perfectly matched layers for advective acoustics. Zbl 0947.76076
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
1999
Galerkin method for wave equations with uncertain coefficients. Zbl 1195.65009
Gottlieb, David; Xiu, Dongbin
2008
On the construction and analysis of absorbing layers in CEM. Zbl 0924.35160
Abarbanel, Saul; Gottlieb, David
1998
Long time behavior of the perfectly matched layer equations in computational electromagnetics. Zbl 1005.78014
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
2002
Recovering pointwise values of discontinuous data within spectral accuracy. Zbl 0597.65099
1985
The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points. Zbl 0815.65106
Don, Wai Sun; Gottlieb, David
1994
Revisiting and extending interface penalties for multi-domain summation-by-parts operators. Zbl 1203.65176
Carpenter, Mark H.; Nordström, Jan; Gottlieb, David
2010
On the Gibbs phenomenon. IV: Recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function. Zbl 0852.42018
Gottlieb, David; Shu, Chi-Wang
1995
Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs. Zbl 1101.65100
Chen, Q.-Y.; Gottlieb, D.; Hesthaven, J. S.
2005
Essentially nonoscillatory spectral Fourier methods for shock wave calculations. Zbl 0666.65067
Cai, Wei; Gottlieb, David; Shu, Chi-Wang
1989
Spectral methods for partial differential equations. (Proceedings of a Symposium, August 16-18, 1982, NASA Langley Research Center, sponsored by the Institute for Computer Applications in Science and Engineering (ICASE)). Zbl 0534.00017
Voigt, Robert G. (ed.); Gottlieb, David (ed.); Hussaini, M. Yousuff (ed.)
1984
Dissipative two-four methods for time-dependent problems. Zbl 0358.65074
Gottlieb, David; Turkel, Eli
1976
Numerical convergence study of nearly incompressible, inviscid Taylor-Green vortex flow. Zbl 1161.76535
Shu, Chi-Wang; Don, Wai-Sun; Gottlieb, David; Schilling, Oleg; Jameson, Leland
2005
Stable and accurate boundary treatments for compact, high-order finite- difference schemes. Zbl 0778.65057
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
1993
The stability of pseudospectral-Chebyshev methods. Zbl 0469.65076
Gottlieb, David
1981
Uncertainty analysis for the steady-state flows in a dual throat nozzle. Zbl 1143.76430
Chen, Qian-Yong; Gottlieb, David; Hesthaven, Jan S.
2005
On the Gibbs phenomenon. V: Recovering exponential accuracy from collocation point values of a piecewise analytic function. Zbl 0852.42019
Gottlieb, David; Shu, Chi-Wang
1995
On the Gibbs phenomenon. III: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function. Zbl 0852.42017
Gottlieb, David; Shu, Chi-Wang
1996
Convergence results for pseudospectral approximations of hyperbolic systems by a penalty-type boundary treatment. Zbl 0736.65074
Funaro, Daniele; Gottlieb, David
1991
On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations. Zbl 0858.65096
Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.
1996
Two-dimensional multi-domain hybrid spectral-WENO methods for conservation laws. Zbl 1114.76050
Costa, B.; Don, W. S.; Gottlieb, D.; Sendersky, R.
2006
Spectral simulations of electromagnetic wave scattering. Zbl 0883.65098
Yang, B.; Gottlieb, D.; Hesthaven, J. S.
1997
On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods. Zbl 0481.65072
Gottlieb, David; Gunzburger, Max; Turkel, Eli
1982
An adaptive pseudo-spectral method for reaction diffusion problems. Zbl 0668.65092
Bayliss, A.; Gottlieb, D.; Matkowsky, B. J.; Minkoff, M.
1989
Stable spectral methods for conservation laws on triangles with unstructured grids. Zbl 0924.76080
Hesthaven, J. S.; Gottlieb, D.
1999
The resolution of the Gibbs phenomenon for “spliced” functions in one and two dimensions. Zbl 0911.65145
Gelb, A.; Gottlieb, D.
1997
Spectral methods for discontinuous problems. Zbl 0646.76082
Abarbanel, S.; Gottlieb, D.; Tadmor, E.
1986
Secondary frequencies in the wake of a circular cylinder with vortex shedding. Zbl 0721.76069
Abarbanel, Saul S.; Don, Wai Sun; Gottlieb, David; Rudy, David H.; Townsend, James C.
1991
Splitting methods for low Mach number Euler and Navier-Stokes equations. Zbl 0664.76088
Abarbanel, Saul; Duth, Pravir; Gottlieb, David
1989
Time-optimal control for a model of bacterial growth. Zbl 0193.48803
D’Ans, G.; Kokotovic, P.; Gottlieb, D.
1971
A multidomain spectral method for supersonic reactive flows. Zbl 1047.76088
Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun
2003
Spectral simulation of supersonic reactive flows. Zbl 0932.76061
Don, Wai Sun; Gottlieb, David
1998
Multiple steady states for characteristic initial value problems. Zbl 0617.76079
Salas, M. D.; Abarbanel, S.; Gottlieb, D.
1986
Stability of pseudospectral and finite-difference methods for variable coefficient problems. Zbl 0537.65084
Gottlieb, David; Orszag, Steven A.; Turkel, Eli
1981
Boundary conditions for multistep finite-difference methods for time- dependent equations. Zbl 0388.65039
Gottlieb, David; Turkel, Eli
1978
The CFL condition for spectral approximations to hyperbolic initial- boundary value problems. Zbl 0723.65079
1991
Numerical stabilizers and computing time for second-order accurate schemes. Zbl 0243.76039
Eilon, B.; Gottlieb, D.; Zwas, G.
1972
Non-linear PML equations for time dependent electromagnetics in three dimensions. Zbl 1176.78035
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
2006
Resolution properties of the Fourier method for discontinuous waves. Zbl 0831.65016
Gottlieb, David; Shu, Chi-Wang
1994
Spectral simulations of an unsteady compressible flow past a circular cylinder. Zbl 0722.76047
Don, Wai-Sun; Gottlieb, David
1990
Topics in spectral methods. Zbl 0564.65074
Gottlieb, David; Turkel, Eli
1985
Difference schemes with fourth order accuracy for hyperbolic equations. Zbl 0325.65041
Abarbanel, S.; Gottlieb, D.; Turkel, E.
1975
Strang-type difference schemes for multidimensional problems. Zbl 0272.65074
Gottlieb, David
1972
Recovering high-order accuracy in WENO computations of steady-state hyperbolic systems. Zbl 1158.76365
Gottlieb, Sigal; Gottlieb, David; Shu, Chi-Wang
2006
On one-sided filters for spectral Fourier approximations of discontinuous functions. Zbl 0755.65140
Cai, Wei; Gottlieb, David; Shu, Chi-Wang
1992
On time discretizations for spectral methods. Zbl 0453.65059
Gottlieb, David; Turkel, Eli
1980
Explicit characterization of spherical curves. Zbl 0206.50201
Breuer, S.; Gottlieb, D.
1971
The reduction of linear ordinary differential equations to equations with constant coefficients. Zbl 0177.11701
Breuer, S.; Gottlieb, D.
1970
Collocation methods for the solution of von-Kármán dynamic nonlinear plate systems. Zbl 1115.74344
Yosibash, Z.; Kirby, R. M.; Gottlieb, D.
2004
On the Engquist Majda absorbing boundary conditions for hyperbolic systems. Zbl 1073.35150
2003
On the convergence of the Fourier approximation for eigenvalues and eigenfunctions of discontinuous problems. Zbl 1036.65087
Min, M. S.; Gottlieb, D.
2003
Mathematical analysis and optimization of infiltration process. Zbl 0933.76089
Chang, H.-C.; Gottlieb, D.; Marion, M.; Sheldon, B. W.
1998
On the conservation and convergence to weak solutions of global schemes. Zbl 1030.65097
Carpenter, Mark H.; Gottlieb, David; Shu, Chi-Wang
2003
A nonlinear Galerkin method: The two-level Fourier-collocation case. Zbl 0859.65111
Dettori, Lucia; Gottlieb, David; Temam, Roger
1995
Cell averaging Chebyshev methods for hyperbolic problems. Zbl 0764.65056
Cai, Wei; Gottlieb, David; Harten, Ami
1992
The DuFort-Frankel Chebyshev method for parabolic initial boundary value problems. Zbl 0511.76003
Gottlieb, David; Lustman, Liviu
1983
Time marching multilevel techniques for evolutionary dissipative problems. Zbl 0995.65106
Costa, B.; Dettori, L.; Gottlieb, D.; Temam, R.
2001
A general theory for the resolution of the Gibbs phenomenon. Zbl 1007.42021
Gottlieb, David; Shu, Chi-Wang
1998
Stability analysis of spectral methods for hyperbolic initial-boundary value systems. Zbl 0628.65109
Gottlieb, David; Lustman, Liviu; Tadmor, Eitan
1987
Spectral methods for compressible flow problems. Zbl 0554.76058
Gottlieb, David
1985
Spectral methods for two-dimensional shocks. Zbl 0567.76068
Gottlieb, David; Lustman, Liviu; Streett, Craig
1984
Generalized DuFort-Frankel methods for parabolic initial-boundary value problems. Zbl 0344.35048
Gottlieb, David; Gustafsson, Bertil
1976
Multidimensional difference schemes with fourth-order accuracy. Zbl 0328.65045
Turkel, E.; Abarbanel, A.; Gottlieb, D.
1976
Upper and lower bounds on eigenvalues of Sturm-Liouville systems. Zbl 0224.34020
Breuer, Shlomo; Gottlieb, David
1971
Spectral methods for compressible reactive flows. Zbl 1223.76117
Gottlieb, David; Gottlieb, Sigal
2005
Optimal decomposition of the domain in spectral methods for wave-like phenomena. Zbl 0967.65102
Wasberg, Carl Erik; Gottlieb, David
2000
On the superconvergence of Galerkin methods for hyperbolic IBVP. Zbl 0858.65094
Gottlieb, David; Gustafsson, Bertil; Olsson, Pelle; Strand, Bo
1996
Convergence of spectral methods for hyperbolic initial-boundary value systems. Zbl 0622.65110
Gottlieb, David; Lustman, Liviu; Tadmor, Eitan
1987
Improving the convergence rate to steady state of parabolic ADI methods. Zbl 0608.65055
Abarbanel, Saul S.; Dwoyer, Douglas L.; Gottlieb, David
1986
Information content in spectral calculations. Zbl 0642.76085
Abarbanel, Saul; Gottlieb, David
1985
A note on the leap-frog scheme in two and three dimensions. Zbl 0331.65057
Abarbanel, Saul; Gottlieb, David
1976
Modified optimal prediction and its application to a particle-method problem. Zbl 1203.65209
Chertock, Alina; Gottlieb, David; Solomonoff, Alex
2008
On the mathematical analysis and optimization of chemical vapor infiltration in materials science. Zbl 0962.76083
Ditkowski, Adi; Gottlieb, David; Sheldon, Brian W.
2000
Implementation of the nonlinear Galerkin method with pseudospectral (collocation) discretizations. Zbl 0782.65122
Gottlieb, David; Temam, Roger
1993
Stability of two-dimensional initial boundary value problems using Leap- Frog type schemes. Zbl 0447.65055
Abarbanel, Saul; Gottlieb, David
1979
Hille-Wintner type oscillation criteria for linear ordinary differential equations of second order. Zbl 0313.34027
Breuer, Shlomo; Gottlieb, David
1975
On proving stability of multidimensional difference schemes. Zbl 0312.65067
Abarbanel, S.; Gottlieb, D.
1975
Domain decomposition spectral approximations for an eigenvalue problem with a piecewise constant coefficient. Zbl 1090.41002
Min, M. S.; Gottlieb, D.
2005
Analysis of the error for approximations to systems of hyperbolic equations. Zbl 0934.65093
Gottlieb, D.; Turkel, E.; Abarbanel, S.
1999
Stability analysis of spectral methods for hyperbolic initial-boundary value systems. Zbl 0755.65099
Gottlieb, David; Lustman, Liviu; Tadmor, Eitan
1988
Convergence of spectral methods for hyperbolic initial-boundary value systems. Zbl 0755.65098
Gottlieb, David; Lustman, Liviu; Tadmor, Eitan
1988
High resolution spectral calculations of inviscid compressible flows. Zbl 0434.35067
Orszag, Steven A.; Gottlieb, David
1980
Revisiting and extending interface penalties for multi-domain summation-by-parts operators. Zbl 1203.65176
Carpenter, Mark H.; Nordström, Jan; Gottlieb, David
2010
A weighted multi-domain spectral penalty method with inhomogeneous grid for supersonic injective cavity flows. Zbl 1364.76146
Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun
2009
Galerkin method for wave equations with uncertain coefficients. Zbl 1195.65009
Gottlieb, David; Xiu, Dongbin
2008
Modified optimal prediction and its application to a particle-method problem. Zbl 1203.65209
Chertock, Alina; Gottlieb, David; Solomonoff, Alex
2008
Spectral methods for time-dependent problems. Zbl 1111.65093
Hesthaven, Jan S.; Gottlieb, Sigal; Gottlieb, David
2007
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes. Zbl 1123.65097
Kanevsky, Alex; Carpenter, Mark H.; Gottlieb, David; Hesthaven, Jan S.
2007
Two-dimensional multi-domain hybrid spectral-WENO methods for conservation laws. Zbl 1114.76050
Costa, B.; Don, W. S.; Gottlieb, D.; Sendersky, R.
2006
Non-linear PML equations for time dependent electromagnetics in three dimensions. Zbl 1176.78035
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
2006
Recovering high-order accuracy in WENO computations of steady-state hyperbolic systems. Zbl 1158.76365
Gottlieb, Sigal; Gottlieb, David; Shu, Chi-Wang
2006
Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs. Zbl 1101.65100
Chen, Q.-Y.; Gottlieb, D.; Hesthaven, J. S.
2005
Numerical convergence study of nearly incompressible, inviscid Taylor-Green vortex flow. Zbl 1161.76535
Shu, Chi-Wang; Don, Wai-Sun; Gottlieb, David; Schilling, Oleg; Jameson, Leland
2005
Uncertainty analysis for the steady-state flows in a dual throat nozzle. Zbl 1143.76430
Chen, Qian-Yong; Gottlieb, David; Hesthaven, Jan S.
2005
Spectral methods for compressible reactive flows. Zbl 1223.76117
Gottlieb, David; Gottlieb, Sigal
2005
Domain decomposition spectral approximations for an eigenvalue problem with a piecewise constant coefficient. Zbl 1090.41002
Min, M. S.; Gottlieb, D.
2005
Foreword. Zbl 1203.65004
Carpenter, Mark H. (ed.); Gottlieb, David I. (ed.); Hesthaven, Jan S. (ed.); Shu, Chi-Wang (ed.)
2005
Collocation methods for the solution of von-Kármán dynamic nonlinear plate systems. Zbl 1115.74344
Yosibash, Z.; Kirby, R. M.; Gottlieb, D.
2004
A multidomain spectral method for supersonic reactive flows. Zbl 1047.76088
Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun
2003
On the Engquist Majda absorbing boundary conditions for hyperbolic systems. Zbl 1073.35150
2003
On the convergence of the Fourier approximation for eigenvalues and eigenfunctions of discontinuous problems. Zbl 1036.65087
Min, M. S.; Gottlieb, D.
2003
On the conservation and convergence to weak solutions of global schemes. Zbl 1030.65097
Carpenter, Mark H.; Gottlieb, David; Shu, Chi-Wang
2003
Long time behavior of the perfectly matched layer equations in computational electromagnetics. Zbl 1005.78014
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
2002
Spectral methods for hyperbolic problems. Zbl 0974.65093
Gottlieb, D.; Hesthaven, J. S.
2001
Time marching multilevel techniques for evolutionary dissipative problems. Zbl 0995.65106
Costa, B.; Dettori, L.; Gottlieb, D.; Temam, R.
2001
Optimal decomposition of the domain in spectral methods for wave-like phenomena. Zbl 0967.65102
Wasberg, Carl Erik; Gottlieb, David
2000
On the mathematical analysis and optimization of chemical vapor infiltration in materials science. Zbl 0962.76083
Ditkowski, Adi; Gottlieb, David; Sheldon, Brian W.
2000
A stable and conservative interface treatment of arbitrary spatial accuracy. Zbl 0921.65059
Carpenter, Mark H.; Nordström, Jan; Gottlieb, David
1999
Well-posed perfectly matched layers for advective acoustics. Zbl 0947.76076
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
1999
Stable spectral methods for conservation laws on triangles with unstructured grids. Zbl 0924.76080
Hesthaven, J. S.; Gottlieb, D.
1999
Analysis of the error for approximations to systems of hyperbolic equations. Zbl 0934.65093
Gottlieb, D.; Turkel, E.; Abarbanel, S.
1999
On the construction and analysis of absorbing layers in CEM. Zbl 0924.35160
Abarbanel, Saul; Gottlieb, David
1998
Spectral simulation of supersonic reactive flows. Zbl 0932.76061
Don, Wai Sun; Gottlieb, David
1998
Mathematical analysis and optimization of infiltration process. Zbl 0933.76089
Chang, H.-C.; Gottlieb, D.; Marion, M.; Sheldon, B. W.
1998
A general theory for the resolution of the Gibbs phenomenon. Zbl 1007.42021
Gottlieb, David; Shu, Chi-Wang
1998
On the Gibbs phenomenon and its resolution. Zbl 0885.42003
Gottlieb, David; Shu, Chi-Wang
1997
A mathematical analysis of the PML method. Zbl 0887.65122
Abarbanel, Saul; Gottlieb, David
1997
Spectral simulations of electromagnetic wave scattering. Zbl 0883.65098
Yang, B.; Gottlieb, D.; Hesthaven, J. S.
1997
The resolution of the Gibbs phenomenon for “spliced” functions in one and two dimensions. Zbl 0911.65145
Gelb, A.; Gottlieb, D.
1997
Spectral methods on arbitrary grids. Zbl 0862.65054
Carpenter, Mark H.; Gottlieb, David
1996
A stable penalty method for the compressible Navier-Stokes equations. I: Open boundary conditions. Zbl 0853.76061
Hesthaven, J. S.; Gottlieb, D.
1996
On the Gibbs phenomenon. III: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function. Zbl 0852.42017
Gottlieb, David; Shu, Chi-Wang
1996
On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations. Zbl 0858.65096
Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.
1996
On the superconvergence of Galerkin methods for hyperbolic IBVP. Zbl 0858.65094
Gottlieb, David; Gustafsson, Bertil; Olsson, Pelle; Strand, Bo
1996
The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A study of the boundary error. Zbl 0839.65098
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun
1995
On the Gibbs phenomenon. IV: Recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function. Zbl 0852.42018
Gottlieb, David; Shu, Chi-Wang
1995
On the Gibbs phenomenon. V: Recovering exponential accuracy from collocation point values of a piecewise analytic function. Zbl 0852.42019
Gottlieb, David; Shu, Chi-Wang
1995
A nonlinear Galerkin method: The two-level Fourier-collocation case. Zbl 0859.65111
Dettori, Lucia; Gottlieb, David; Temam, Roger
1995
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. Zbl 0832.65098
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
1994
The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points. Zbl 0815.65106
Don, Wai Sun; Gottlieb, David
1994
Resolution properties of the Fourier method for discontinuous waves. Zbl 0831.65016
Gottlieb, David; Shu, Chi-Wang
1994
The stability of numerical boundary treatments for compact high-order finite-difference schemes. Zbl 0791.76052
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
1993
Stable and accurate boundary treatments for compact, high-order finite- difference schemes. Zbl 0778.65057
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
1993
Implementation of the nonlinear Galerkin method with pseudospectral (collocation) discretizations. Zbl 0782.65122
Gottlieb, David; Temam, Roger
1993
On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function. Zbl 0781.42022
Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Hervé
1992
On one-sided filters for spectral Fourier approximations of discontinuous functions. Zbl 0755.65140
Cai, Wei; Gottlieb, David; Shu, Chi-Wang
1992
Cell averaging Chebyshev methods for hyperbolic problems. Zbl 0764.65056
Cai, Wei; Gottlieb, David; Harten, Ami
1992
Convergence results for pseudospectral approximations of hyperbolic systems by a penalty-type boundary treatment. Zbl 0736.65074
Funaro, Daniele; Gottlieb, David
1991
Secondary frequencies in the wake of a circular cylinder with vortex shedding. Zbl 0721.76069
Abarbanel, Saul S.; Don, Wai Sun; Gottlieb, David; Rudy, David H.; Townsend, James C.
1991
The CFL condition for spectral approximations to hyperbolic initial- boundary value problems. Zbl 0723.65079
1991
Spectral simulations of an unsteady compressible flow past a circular cylinder. Zbl 0722.76047
Don, Wai-Sun; Gottlieb, David
1990
Quadrature imposition of compatibility conditions in Chebyshev methods. Zbl 0725.76060
Gottlieb, D.; Streett, C. L.
1990
Essentially nonoscillatory spectral Fourier methods for shock wave calculations. Zbl 0666.65067
Cai, Wei; Gottlieb, David; Shu, Chi-Wang
1989
An adaptive pseudo-spectral method for reaction diffusion problems. Zbl 0668.65092
Bayliss, A.; Gottlieb, D.; Matkowsky, B. J.; Minkoff, M.
1989
Splitting methods for low Mach number Euler and Navier-Stokes equations. Zbl 0664.76088
Abarbanel, Saul; Duth, Pravir; Gottlieb, David
1989
A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations. Zbl 0699.65079
Funaro, D.; Gottlieb, D.
1988
Stability analysis of spectral methods for hyperbolic initial-boundary value systems. Zbl 0755.65099
Gottlieb, David; Lustman, Liviu; Tadmor, Eitan
1988
Convergence of spectral methods for hyperbolic initial-boundary value systems. Zbl 0755.65098
Gottlieb, David; Lustman, Liviu; Tadmor, Eitan
1988
Stability analysis of spectral methods for hyperbolic initial-boundary value systems. Zbl 0628.65109
Gottlieb, David; Lustman, Liviu; Tadmor, Eitan
1987
Convergence of spectral methods for hyperbolic initial-boundary value systems. Zbl 0622.65110
Gottlieb, David; Lustman, Liviu; Tadmor, Eitan
1987
Spectral methods for discontinuous problems. Zbl 0646.76082
Abarbanel, S.; Gottlieb, D.; Tadmor, E.
1986
Multiple steady states for characteristic initial value problems. Zbl 0617.76079
Salas, M. D.; Abarbanel, S.; Gottlieb, D.
1986
Improving the convergence rate to steady state of parabolic ADI methods. Zbl 0608.65055
Abarbanel, Saul S.; Dwoyer, Douglas L.; Gottlieb, David
1986
Recovering pointwise values of discontinuous data within spectral accuracy. Zbl 0597.65099
1985
Topics in spectral methods. Zbl 0564.65074
Gottlieb, David; Turkel, Eli
1985
Spectral methods for compressible flow problems. Zbl 0554.76058
Gottlieb, David
1985
Information content in spectral calculations. Zbl 0642.76085
Abarbanel, Saul; Gottlieb, David
1985
Theory and applications of spectral methods. Zbl 0599.65079
Gottlieb, David; Hussaini, M. Yousuff; Orszag, Steven A.
1984
Spectral methods for partial differential equations. (Proceedings of a Symposium, August 16-18, 1982, NASA Langley Research Center, sponsored by the Institute for Computer Applications in Science and Engineering (ICASE)). Zbl 0534.00017
Voigt, Robert G. (ed.); Gottlieb, David (ed.); Hussaini, M. Yousuff (ed.)
1984
Spectral methods for two-dimensional shocks. Zbl 0567.76068
Gottlieb, David; Lustman, Liviu; Streett, Craig
1984
The spectrum of the Chebyshev collocation operator for the heat equation. Zbl 0537.65085
Gottlieb, David; Lustman, Liviu
1983
The DuFort-Frankel Chebyshev method for parabolic initial boundary value problems. Zbl 0511.76003
Gottlieb, David; Lustman, Liviu
1983
On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods. Zbl 0481.65072
Gottlieb, David; Gunzburger, Max; Turkel, Eli
1982
Spectral computations of one dimensional inviscid compressible flows. Zbl 0561.76076
Gottlieb, D.; Lustman, L.; Orszag, S. A.
1981
Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives. Zbl 0467.76062
Abarbanel, Saul; Gottlieb, David
1981
The stability of pseudospectral-Chebyshev methods. Zbl 0469.65076
Gottlieb, David
1981
Stability of pseudospectral and finite-difference methods for variable coefficient problems. Zbl 0537.65084
Gottlieb, David; Orszag, Steven A.; Turkel, Eli
1981
On time discretizations for spectral methods. Zbl 0453.65059
Gottlieb, David; Turkel, Eli
1980
High resolution spectral calculations of inviscid compressible flows. Zbl 0434.35067
Orszag, Steven A.; Gottlieb, David
1980
Stability of two-dimensional initial boundary value problems using Leap- Frog type schemes. Zbl 0447.65055
Abarbanel, Saul; Gottlieb, David
1979
Boundary conditions for multistep finite-difference methods for time- dependent equations. Zbl 0388.65039
Gottlieb, David; Turkel, Eli
1978
Numerical analysis of spectral methods: Theory and applications. Zbl 0412.65058
Gottlieb, David; Orszag, Steven A.
1977
Dissipative two-four methods for time-dependent problems. Zbl 0358.65074
Gottlieb, David; Turkel, Eli
1976
Generalized DuFort-Frankel methods for parabolic initial-boundary value problems. Zbl 0344.35048
Gottlieb, David; Gustafsson, Bertil
1976
Multidimensional difference schemes with fourth-order accuracy. Zbl 0328.65045
Turkel, E.; Abarbanel, A.; Gottlieb, D.
1976
A note on the leap-frog scheme in two and three dimensions. Zbl 0331.65057
Abarbanel, Saul; Gottlieb, David
1976
On the Navier-Stokes equations with constant total temperature. Zbl 0342.76025
Gottlieb, David; Gustafsson, Bertil
1976
Difference schemes with fourth order accuracy for hyperbolic equations. Zbl 0325.65041
Abarbanel, S.; Gottlieb, D.; Turkel, E.
1975
Hille-Wintner type oscillation criteria for linear ordinary differential equations of second order. Zbl 0313.34027
Breuer, Shlomo; Gottlieb, David
1975
On proving stability of multidimensional difference schemes. Zbl 0312.65067
Abarbanel, S.; Gottlieb, D.
1975
Phase error and stability of second order methods for hyperbolic problems. II. Zbl 0284.65078
Gottlieb, David; Turkel, Eli
1974
Higher order accuracy finite difference algorithms for quasi-linear, conservation law hyperbolic systems. Zbl 0293.65072
Abarbanel, S.; Gottlieb, D.
1973
...and 8 more Documents
all top 5

#### Cited by 3,352 Authors

 86 Nordström, Jan 38 Guo, Ben-Yu 34 Hesthaven, Jan S. 33 Boyd, John Philip 32 Gottlieb, David I. 31 Shu, Chi-Wang 29 Karniadakis, George Em 28 Carpenter, Mark H. 27 Dehghan Takht Fooladi, Mehdi 26 Gelb, Anne 25 Mattsson, Ken 24 Doha, Eid H. 24 Nicholls, David P. 22 Turkel, Eli L. 21 Shen, Jie 19 Wang, Lilian 18 Jung, Jae-Hun 17 Heinrichs, Wilhelm 17 Svärd, Magnus 17 Zingg, David W. 15 Funaro, Daniele 15 Kreiss, Gunilla 14 Del Rey Fernández, David C. 14 Wang, Cheng 13 Gottlieb, Sigal 13 Kopriva, David Alan 13 Shizgal, Bernie D. 12 Abd-Elhameed, Waleed Mohamed 12 Bhrawy, Ali Hassan 12 Ditkowski, Adi 12 Sherwin, Spencer J. 11 Abarbanel, Saul S. 11 Bruno, Oscar P. 11 Canuto, Claudio 11 Don, Wai Sun 11 Gassner, Gregor J. 11 Hicken, Jason E. 11 Maday, Yvon 11 Quarteroni, Alfio M. 11 Sandham, Neil D. 11 Tadmor, Eitan 11 Wang, Zhongqing 10 Amat, Sergio P. 10 Bayliss, Alvin 10 Hejranfar, Kazem 10 Karageorghis, Andreas 10 Ma, Heping 10 Sjogreen, Bjorn 10 Venturi, Daniele 10 Xiu, Dongbin 9 Adcock, Ben 9 Deville, Michel O. 9 Dunham, Eric M. 9 Gottlieb, David 9 Jin, Shi 9 Temam, Roger Meyer 9 Tsynkov, Semyon V. 8 Almquist, Martin 8 Bao, Weizhu 8 Cai, Wei 8 Duru, Kenneth 8 Elbarbary, Elsayed M. E. M. 8 Hu, Fang Qi 8 Jacobs, Gustaaf B. 8 Kirby, Robert M. II 8 Labrosse, Gérard 8 Mishra, Siddhartha 8 Mokhtary, Payam 8 Phillips, Timothy N. 8 Pullin, Dale I. 8 Sandberg, Richard D. 8 Wang, Tianjun 8 Xiang, Shuhuang 8 Yee, Helen C. 7 Berg, Jens 7 Cheng, Kelong 7 Elgindy, Kareem T. 7 Fischer, Paul F. 7 Ghoreishi, Farideh 7 Hagstrom, Thomas M. 7 Hosseini, Seyed Mohammad 7 Huang, Jingfang 7 Iaccarino, Gianluca 7 Li, Huiyuan 7 Li, Jichun 7 Lundquist, Tomas 7 Matkowsky, Bernard J. 7 Minion, Michael L. 7 O’Reilly, Ossian 7 Orszag, Steven Alan 7 Pantano, Carlos 7 Petersson, N. Anders 7 Quartapelle, Luigi 7 Trillo, Juan Carlos 7 Wang, Siyang 7 Winters, Andrew R. 7 Zampieri, Elena 7 Zhang, Mengping 6 Beris, Antony N. 6 Diamessis, Peter J. ...and 3,252 more Authors
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#### Cited in 233 Serials

 684 Journal of Computational Physics 250 Journal of Scientific Computing 131 Journal of Computational and Applied Mathematics 120 Applied Numerical Mathematics 102 Computer Methods in Applied Mechanics and Engineering 85 Computers and Fluids 83 Applied Mathematics and Computation 69 Mathematics of Computation 62 Computers & Mathematics with Applications 44 SIAM Journal on Scientific Computing 37 Journal of Fluid Mechanics 31 Numerical Algorithms 30 Applied Mathematical Modelling 29 Physica D 28 Numerische Mathematik 26 Computer Physics Communications 24 Journal of Mathematical Analysis and Applications 23 International Journal of Computer Mathematics 19 SIAM Journal on Numerical Analysis 17 International Journal for Numerical Methods in Fluids 16 Theoretical and Computational Fluid Dynamics 16 BIT 16 Numerical Methods for Partial Differential Equations 15 International Journal for Numerical Methods in Engineering 15 Mathematics and Computers in Simulation 14 Mathematical and Computer Modelling 14 Applied and Computational Harmonic Analysis 14 International Journal of Computational Fluid Dynamics 13 Applied Mathematics Letters 13 Physics of Fluids 13 Advances in Computational Mathematics 12 Mathematical Methods in the Applied Sciences 11 Calcolo 11 Communications in Nonlinear Science and Numerical Simulation 10 Wave Motion 10 Mathematical Problems in Engineering 9 Proceedings of the American Mathematical Society 9 Computational Mechanics 8 Journal of Engineering Mathematics 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Acta Mechanica 7 Automatica 7 RAIRO. Modélisation Mathématique et Analyse Numérique 7 Computational and Applied Mathematics 6 Physics of Fluids 6 Engineering Analysis with Boundary Elements 6 Living Reviews in Relativity 6 S$$\vec{\text{e}}$$MA Journal 6 SIAM/ASA Journal on Uncertainty Quantification 5 Nonlinear Dynamics 5 Advances in Difference Equations 5 Journal of Computational Acoustics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Journal of Approximation Theory 4 Numerical Functional Analysis and Optimization 4 Applied Mathematics and Mechanics. (English Edition) 4 Linear Algebra and its Applications 4 Archive of Applied Mechanics 4 Communications in Numerical Methods in Engineering 4 International Journal of Numerical Methods for Heat & Fluid Flow 4 Abstract and Applied Analysis 4 European Journal of Mechanics. A. Solids 4 Archives of Computational Methods in Engineering 4 Foundations of Computational Mathematics 4 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Applied Mathematics and Computing 4 International Journal of Computational Methods 3 Applicable Analysis 3 International Journal of Control 3 International Journal of Heat and Mass Transfer 3 Journal of the Franklin Institute 3 Journal of Mathematical Physics 3 Journal of Statistical Physics 3 Transport Theory and Statistical Physics 3 Journal of Optimization Theory and Applications 3 Quarterly of Applied Mathematics 3 Studies in Applied Mathematics 3 Bulletin of the Iranian Mathematical Society 3 Acta Mathematicae Applicatae Sinica. English Series 3 COMPEL 3 Integral Transforms and Special Functions 3 The Journal of Fourier Analysis and Applications 3 Journal of Mathematical Chemistry 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 European Journal of Mechanics. B. Fluids 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Computational Geosciences 3 Journal of Applied Mathematics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 International Journal of Advances in Engineering Sciences and Applied Mathematics 2 Archive for Rational Mechanics and Analysis 2 Geophysical and Astrophysical Fluid Dynamics 2 General Relativity and Gravitation 2 International Journal of Engineering Science 2 Mathematical Biosciences 2 Physics Letters. A 2 Chaos, Solitons and Fractals 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of Differential Equations 2 RAIRO. Analyse Numérique ...and 133 more Serials
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#### Cited in 42 Fields

 1,738 Numerical analysis (65-XX) 919 Fluid mechanics (76-XX) 847 Partial differential equations (35-XX) 166 Ordinary differential equations (34-XX) 120 Mechanics of deformable solids (74-XX) 114 Harmonic analysis on Euclidean spaces (42-XX) 113 Approximations and expansions (41-XX) 111 Optics, electromagnetic theory (78-XX) 75 Special functions (33-XX) 56 Classical thermodynamics, heat transfer (80-XX) 54 Statistical mechanics, structure of matter (82-XX) 53 Integral equations (45-XX) 51 Geophysics (86-XX) 46 Probability theory and stochastic processes (60-XX) 46 Biology and other natural sciences (92-XX) 41 Calculus of variations and optimal control; optimization (49-XX) 33 Quantum theory (81-XX) 32 Systems theory; control (93-XX) 30 Dynamical systems and ergodic theory (37-XX) 25 Information and communication theory, circuits (94-XX) 21 Relativity and gravitational theory (83-XX) 19 Operations research, mathematical programming (90-XX) 18 Statistics (62-XX) 17 Functions of a complex variable (30-XX) 17 Astronomy and astrophysics (85-XX) 16 Real functions (26-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 13 Computer science (68-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Differential geometry (53-XX) 10 Operator theory (47-XX) 8 Potential theory (31-XX) 8 Integral transforms, operational calculus (44-XX) 7 Mechanics of particles and systems (70-XX) 6 History and biography (01-XX) 4 General and overarching topics; collections (00-XX) 4 Difference and functional equations (39-XX) 4 Functional analysis (46-XX) 3 Number theory (11-XX) 3 Global analysis, analysis on manifolds (58-XX) 1 Commutative algebra (13-XX) 1 Measure and integration (28-XX)

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