Edit Profile Gottlieb, David I. Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0412.65058Gottlieb, David; Orszag, Steven A. 931 1977 Spectral methods for time-dependent problems. Zbl 1111.65093Hesthaven, Jan S.; Gottlieb, Sigal; Gottlieb, David 296 2007 Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. Zbl 0832.65098Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul 216 1994 On the Gibbs phenomenon and its resolution. Zbl 0885.42003Gottlieb, David; Shu, Chi-Wang 192 1997 A stable and conservative interface treatment of arbitrary spatial accuracy. Zbl 0921.65059Carpenter, Mark H.; Nordström, Jan; Gottlieb, David 136 1999 The stability of numerical boundary treatments for compact high-order finite-difference schemes. Zbl 0791.76052Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul 117 1993 Spectral methods for hyperbolic problems. Zbl 0974.65093Gottlieb, D.; Hesthaven, J. S. 94 2001 Theory and applications of spectral methods. Zbl 0599.65079Gottlieb, David; Hussaini, M. Yousuff; Orszag, Steven A. 91 1984 Spectral computations of one dimensional inviscid compressible flows. Zbl 0561.76076Gottlieb, D.; Lustman, L.; Orszag, S. A. 78 1981 A mathematical analysis of the PML method. Zbl 0887.65122Abarbanel, Saul; Gottlieb, David 70 1997 On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function. Zbl 0781.42022Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Hervé 70 1992 The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A study of the boundary error. Zbl 0839.65098Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun 63 1995 Spectral methods on arbitrary grids. Zbl 0862.65054Carpenter, Mark H.; Gottlieb, David 62 1996 A stable penalty method for the compressible Navier-Stokes equations. I: Open boundary conditions. Zbl 0853.76061Hesthaven, J. S.; Gottlieb, D. 55 1996 The spectrum of the Chebyshev collocation operator for the heat equation. Zbl 0537.65085Gottlieb, David; Lustman, Liviu 50 1983 Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives. Zbl 0467.76062Abarbanel, Saul; Gottlieb, David 49 1981 A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations. Zbl 0699.65079Funaro, D.; Gottlieb, D. 48 1988 Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes. Zbl 1123.65097Kanevsky, Alex; Carpenter, Mark H.; Gottlieb, David; Hesthaven, Jan S. 46 2007 Well-posed perfectly matched layers for advective acoustics. Zbl 0947.76076Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S. 43 1999 Galerkin method for wave equations with uncertain coefficients. Zbl 1195.65009Gottlieb, David; Xiu, Dongbin 42 2008 On the construction and analysis of absorbing layers in CEM. Zbl 0924.35160Abarbanel, Saul; Gottlieb, David 42 1998 Long time behavior of the perfectly matched layer equations in computational electromagnetics. Zbl 1005.78014Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S. 39 2002 Recovering pointwise values of discontinuous data within spectral accuracy. Zbl 0597.65099Gottlieb, David; Tadmor, Eitan 38 1985 The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points. Zbl 0815.65106Don, Wai Sun; Gottlieb, David 34 1994 Revisiting and extending interface penalties for multi-domain summation-by-parts operators. Zbl 1203.65176Carpenter, Mark H.; Nordström, Jan; Gottlieb, David 33 2010 On the Gibbs phenomenon. IV: Recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function. Zbl 0852.42018Gottlieb, David; Shu, Chi-Wang 33 1995 Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs. Zbl 1101.65100Chen, Q.-Y.; Gottlieb, D.; Hesthaven, J. S. 32 2005 Essentially nonoscillatory spectral Fourier methods for shock wave calculations. Zbl 0666.65067Cai, Wei; Gottlieb, David; Shu, Chi-Wang 32 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 0534.00017Voigt, Robert G. (ed.); Gottlieb, David (ed.); Hussaini, M. Yousuff (ed.) 32 1984 Dissipative two-four methods for time-dependent problems. Zbl 0358.65074Gottlieb, David; Turkel, Eli 29 1976 Numerical convergence study of nearly incompressible, inviscid Taylor-Green vortex flow. Zbl 1161.76535Shu, Chi-Wang; Don, Wai-Sun; Gottlieb, David; Schilling, Oleg; Jameson, Leland 28 2005 Stable and accurate boundary treatments for compact, high-order finite- difference schemes. Zbl 0778.65057Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul 26 1993 The stability of pseudospectral-Chebyshev methods. Zbl 0469.65076Gottlieb, David 26 1981 Uncertainty analysis for the steady-state flows in a dual throat nozzle. Zbl 1143.76430Chen, Qian-Yong; Gottlieb, David; Hesthaven, Jan S. 24 2005 On the Gibbs phenomenon. V: Recovering exponential accuracy from collocation point values of a piecewise analytic function. Zbl 0852.42019Gottlieb, David; Shu, Chi-Wang 24 1995 On the Gibbs phenomenon. III: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function. Zbl 0852.42017Gottlieb, David; Shu, Chi-Wang 23 1996 Convergence results for pseudospectral approximations of hyperbolic systems by a penalty-type boundary treatment. Zbl 0736.65074Funaro, Daniele; Gottlieb, David 23 1991 On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations. Zbl 0858.65096Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H. 22 1996 Two-dimensional multi-domain hybrid spectral-WENO methods for conservation laws. Zbl 1114.76050Costa, B.; Don, W. S.; Gottlieb, D.; Sendersky, R. 20 2006 Spectral simulations of electromagnetic wave scattering. Zbl 0883.65098Yang, B.; Gottlieb, D.; Hesthaven, J. S. 20 1997 On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods. Zbl 0481.65072Gottlieb, David; Gunzburger, Max; Turkel, Eli 20 1982 An adaptive pseudo-spectral method for reaction diffusion problems. Zbl 0668.65092Bayliss, A.; Gottlieb, D.; Matkowsky, B. J.; Minkoff, M. 18 1989 Stable spectral methods for conservation laws on triangles with unstructured grids. Zbl 0924.76080Hesthaven, J. S.; Gottlieb, D. 16 1999 The resolution of the Gibbs phenomenon for “spliced” functions in one and two dimensions. Zbl 0911.65145Gelb, A.; Gottlieb, D. 16 1997 Spectral methods for discontinuous problems. Zbl 0646.76082Abarbanel, S.; Gottlieb, D.; Tadmor, E. 14 1986 Secondary frequencies in the wake of a circular cylinder with vortex shedding. Zbl 0721.76069Abarbanel, Saul S.; Don, Wai Sun; Gottlieb, David; Rudy, David H.; Townsend, James C. 13 1991 Splitting methods for low Mach number Euler and Navier-Stokes equations. Zbl 0664.76088Abarbanel, Saul; Duth, Pravir; Gottlieb, David 13 1989 Time-optimal control for a model of bacterial growth. Zbl 0193.48803D’Ans, G.; Kokotovic, P.; Gottlieb, D. 13 1971 A multidomain spectral method for supersonic reactive flows. Zbl 1047.76088Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun 12 2003 Spectral simulation of supersonic reactive flows. Zbl 0932.76061Don, Wai Sun; Gottlieb, David 12 1998 Multiple steady states for characteristic initial value problems. Zbl 0617.76079Salas, M. D.; Abarbanel, S.; Gottlieb, D. 12 1986 Stability of pseudospectral and finite-difference methods for variable coefficient problems. Zbl 0537.65084Gottlieb, David; Orszag, Steven A.; Turkel, Eli 12 1981 Boundary conditions for multistep finite-difference methods for time- dependent equations. Zbl 0388.65039Gottlieb, David; Turkel, Eli 12 1978 The CFL condition for spectral approximations to hyperbolic initial- boundary value problems. Zbl 0723.65079Gottlieb, David; Tadmor, Eitan 11 1991 Numerical stabilizers and computing time for second-order accurate schemes. Zbl 0243.76039Eilon, B.; Gottlieb, D.; Zwas, G. 11 1972 Non-linear PML equations for time dependent electromagnetics in three dimensions. Zbl 1176.78035Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S. 10 2006 Resolution properties of the Fourier method for discontinuous waves. Zbl 0831.65016Gottlieb, David; Shu, Chi-Wang 10 1994 Spectral simulations of an unsteady compressible flow past a circular cylinder. Zbl 0722.76047Don, Wai-Sun; Gottlieb, David 9 1990 Topics in spectral methods. Zbl 0564.65074Gottlieb, David; Turkel, Eli 9 1985 Difference schemes with fourth order accuracy for hyperbolic equations. Zbl 0325.65041Abarbanel, S.; Gottlieb, D.; Turkel, E. 9 1975 Strang-type difference schemes for multidimensional problems. Zbl 0272.65074Gottlieb, David 9 1972 Recovering high-order accuracy in WENO computations of steady-state hyperbolic systems. Zbl 1158.76365Gottlieb, Sigal; Gottlieb, David; Shu, Chi-Wang 8 2006 On one-sided filters for spectral Fourier approximations of discontinuous functions. Zbl 0755.65140Cai, Wei; Gottlieb, David; Shu, Chi-Wang 8 1992 On time discretizations for spectral methods. Zbl 0453.65059Gottlieb, David; Turkel, Eli 8 1980 Explicit characterization of spherical curves. Zbl 0206.50201Breuer, S.; Gottlieb, D. 8 1971 The reduction of linear ordinary differential equations to equations with constant coefficients. Zbl 0177.11701Breuer, S.; Gottlieb, D. 8 1970 Collocation methods for the solution of von-Kármán dynamic nonlinear plate systems. Zbl 1115.74344Yosibash, Z.; Kirby, R. M.; Gottlieb, D. 7 2004 On the Engquist Majda absorbing boundary conditions for hyperbolic systems. Zbl 1073.35150Ditkowski, Adi; Gottlieb, David 7 2003 On the convergence of the Fourier approximation for eigenvalues and eigenfunctions of discontinuous problems. Zbl 1036.65087Min, M. S.; Gottlieb, D. 7 2003 Mathematical analysis and optimization of infiltration process. Zbl 0933.76089Chang, H.-C.; Gottlieb, D.; Marion, M.; Sheldon, B. W. 7 1998 On the conservation and convergence to weak solutions of global schemes. Zbl 1030.65097Carpenter, Mark H.; Gottlieb, David; Shu, Chi-Wang 6 2003 A nonlinear Galerkin method: The two-level Fourier-collocation case. Zbl 0859.65111Dettori, Lucia; Gottlieb, David; Temam, Roger 6 1995 Cell averaging Chebyshev methods for hyperbolic problems. Zbl 0764.65056Cai, Wei; Gottlieb, David; Harten, Ami 6 1992 The DuFort-Frankel Chebyshev method for parabolic initial boundary value problems. Zbl 0511.76003Gottlieb, David; Lustman, Liviu 6 1983 Time marching multilevel techniques for evolutionary dissipative problems. Zbl 0995.65106Costa, B.; Dettori, L.; Gottlieb, D.; Temam, R. 5 2001 A general theory for the resolution of the Gibbs phenomenon. Zbl 1007.42021Gottlieb, David; Shu, Chi-Wang 5 1998 Stability analysis of spectral methods for hyperbolic initial-boundary value systems. Zbl 0628.65109Gottlieb, David; Lustman, Liviu; Tadmor, Eitan 5 1987 Spectral methods for compressible flow problems. Zbl 0554.76058Gottlieb, David 5 1985 Spectral methods for two-dimensional shocks. Zbl 0567.76068Gottlieb, David; Lustman, Liviu; Streett, Craig 5 1984 Generalized DuFort-Frankel methods for parabolic initial-boundary value problems. Zbl 0344.35048Gottlieb, David; Gustafsson, Bertil 5 1976 Multidimensional difference schemes with fourth-order accuracy. Zbl 0328.65045Turkel, E.; Abarbanel, A.; Gottlieb, D. 5 1976 Upper and lower bounds on eigenvalues of Sturm-Liouville systems. Zbl 0224.34020Breuer, Shlomo; Gottlieb, David 5 1971 Spectral methods for compressible reactive flows. Zbl 1223.76117Gottlieb, David; Gottlieb, Sigal 4 2005 Optimal decomposition of the domain in spectral methods for wave-like phenomena. Zbl 0967.65102Wasberg, Carl Erik; Gottlieb, David 4 2000 On the superconvergence of Galerkin methods for hyperbolic IBVP. Zbl 0858.65094Gottlieb, David; Gustafsson, Bertil; Olsson, Pelle; Strand, Bo 4 1996 Convergence of spectral methods for hyperbolic initial-boundary value systems. Zbl 0622.65110Gottlieb, David; Lustman, Liviu; Tadmor, Eitan 4 1987 Improving the convergence rate to steady state of parabolic ADI methods. Zbl 0608.65055Abarbanel, Saul S.; Dwoyer, Douglas L.; Gottlieb, David 4 1986 Information content in spectral calculations. Zbl 0642.76085Abarbanel, Saul; Gottlieb, David 4 1985 A note on the leap-frog scheme in two and three dimensions. Zbl 0331.65057Abarbanel, Saul; Gottlieb, David 4 1976 Modified optimal prediction and its application to a particle-method problem. Zbl 1203.65209Chertock, Alina; Gottlieb, David; Solomonoff, Alex 3 2008 On the mathematical analysis and optimization of chemical vapor infiltration in materials science. Zbl 0962.76083Ditkowski, Adi; Gottlieb, David; Sheldon, Brian W. 3 2000 Implementation of the nonlinear Galerkin method with pseudospectral (collocation) discretizations. Zbl 0782.65122Gottlieb, David; Temam, Roger 3 1993 Stability of two-dimensional initial boundary value problems using Leap- Frog type schemes. Zbl 0447.65055Abarbanel, Saul; Gottlieb, David 3 1979 Hille-Wintner type oscillation criteria for linear ordinary differential equations of second order. Zbl 0313.34027Breuer, Shlomo; Gottlieb, David 3 1975 On proving stability of multidimensional difference schemes. Zbl 0312.65067Abarbanel, S.; Gottlieb, D. 3 1975 Domain decomposition spectral approximations for an eigenvalue problem with a piecewise constant coefficient. Zbl 1090.41002Min, M. S.; Gottlieb, D. 2 2005 Analysis of the error for approximations to systems of hyperbolic equations. Zbl 0934.65093Gottlieb, D.; Turkel, E.; Abarbanel, S. 2 1999 Stability analysis of spectral methods for hyperbolic initial-boundary value systems. Zbl 0755.65099Gottlieb, David; Lustman, Liviu; Tadmor, Eitan 2 1988 Convergence of spectral methods for hyperbolic initial-boundary value systems. Zbl 0755.65098Gottlieb, David; Lustman, Liviu; Tadmor, Eitan 2 1988 High resolution spectral calculations of inviscid compressible flows. Zbl 0434.35067Orszag, Steven A.; Gottlieb, David 2 1980 Revisiting and extending interface penalties for multi-domain summation-by-parts operators. Zbl 1203.65176Carpenter, Mark H.; Nordström, Jan; Gottlieb, David 33 2010 A weighted multi-domain spectral penalty method with inhomogeneous grid for supersonic injective cavity flows. Zbl 1364.76146Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun 1 2009 Galerkin method for wave equations with uncertain coefficients. Zbl 1195.65009Gottlieb, David; Xiu, Dongbin 42 2008 Modified optimal prediction and its application to a particle-method problem. Zbl 1203.65209Chertock, Alina; Gottlieb, David; Solomonoff, Alex 3 2008 Spectral methods for time-dependent problems. Zbl 1111.65093Hesthaven, Jan S.; Gottlieb, Sigal; Gottlieb, David 296 2007 Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes. Zbl 1123.65097Kanevsky, Alex; Carpenter, Mark H.; Gottlieb, David; Hesthaven, Jan S. 46 2007 Two-dimensional multi-domain hybrid spectral-WENO methods for conservation laws. Zbl 1114.76050Costa, B.; Don, W. S.; Gottlieb, D.; Sendersky, R. 20 2006 Non-linear PML equations for time dependent electromagnetics in three dimensions. Zbl 1176.78035Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S. 10 2006 Recovering high-order accuracy in WENO computations of steady-state hyperbolic systems. Zbl 1158.76365Gottlieb, Sigal; Gottlieb, David; Shu, Chi-Wang 8 2006 Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs. Zbl 1101.65100Chen, Q.-Y.; Gottlieb, D.; Hesthaven, J. S. 32 2005 Numerical convergence study of nearly incompressible, inviscid Taylor-Green vortex flow. Zbl 1161.76535Shu, Chi-Wang; Don, Wai-Sun; Gottlieb, David; Schilling, Oleg; Jameson, Leland 28 2005 Uncertainty analysis for the steady-state flows in a dual throat nozzle. Zbl 1143.76430Chen, Qian-Yong; Gottlieb, David; Hesthaven, Jan S. 24 2005 Spectral methods for compressible reactive flows. Zbl 1223.76117Gottlieb, David; Gottlieb, Sigal 4 2005 Domain decomposition spectral approximations for an eigenvalue problem with a piecewise constant coefficient. Zbl 1090.41002Min, M. S.; Gottlieb, D. 2 2005 Foreword. Zbl 1203.65004Carpenter, Mark H. (ed.); Gottlieb, David I. (ed.); Hesthaven, Jan S. (ed.); Shu, Chi-Wang (ed.) 1 2005 Collocation methods for the solution of von-Kármán dynamic nonlinear plate systems. Zbl 1115.74344Yosibash, Z.; Kirby, R. M.; Gottlieb, D. 7 2004 A multidomain spectral method for supersonic reactive flows. Zbl 1047.76088Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun 12 2003 On the Engquist Majda absorbing boundary conditions for hyperbolic systems. Zbl 1073.35150Ditkowski, Adi; Gottlieb, David 7 2003 On the convergence of the Fourier approximation for eigenvalues and eigenfunctions of discontinuous problems. Zbl 1036.65087Min, M. S.; Gottlieb, D. 7 2003 On the conservation and convergence to weak solutions of global schemes. Zbl 1030.65097Carpenter, Mark H.; Gottlieb, David; Shu, Chi-Wang 6 2003 Long time behavior of the perfectly matched layer equations in computational electromagnetics. Zbl 1005.78014Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S. 39 2002 Spectral methods for hyperbolic problems. Zbl 0974.65093Gottlieb, D.; Hesthaven, J. S. 94 2001 Time marching multilevel techniques for evolutionary dissipative problems. Zbl 0995.65106Costa, B.; Dettori, L.; Gottlieb, D.; Temam, R. 5 2001 Optimal decomposition of the domain in spectral methods for wave-like phenomena. Zbl 0967.65102Wasberg, Carl Erik; Gottlieb, David 4 2000 On the mathematical analysis and optimization of chemical vapor infiltration in materials science. Zbl 0962.76083Ditkowski, Adi; Gottlieb, David; Sheldon, Brian W. 3 2000 A stable and conservative interface treatment of arbitrary spatial accuracy. Zbl 0921.65059Carpenter, Mark H.; Nordström, Jan; Gottlieb, David 136 1999 Well-posed perfectly matched layers for advective acoustics. Zbl 0947.76076Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S. 43 1999 Stable spectral methods for conservation laws on triangles with unstructured grids. Zbl 0924.76080Hesthaven, J. S.; Gottlieb, D. 16 1999 Analysis of the error for approximations to systems of hyperbolic equations. Zbl 0934.65093Gottlieb, D.; Turkel, E.; Abarbanel, S. 2 1999 On the construction and analysis of absorbing layers in CEM. Zbl 0924.35160Abarbanel, Saul; Gottlieb, David 42 1998 Spectral simulation of supersonic reactive flows. Zbl 0932.76061Don, Wai Sun; Gottlieb, David 12 1998 Mathematical analysis and optimization of infiltration process. Zbl 0933.76089Chang, H.-C.; Gottlieb, D.; Marion, M.; Sheldon, B. W. 7 1998 A general theory for the resolution of the Gibbs phenomenon. Zbl 1007.42021Gottlieb, David; Shu, Chi-Wang 5 1998 On the Gibbs phenomenon and its resolution. Zbl 0885.42003Gottlieb, David; Shu, Chi-Wang 192 1997 A mathematical analysis of the PML method. Zbl 0887.65122Abarbanel, Saul; Gottlieb, David 70 1997 Spectral simulations of electromagnetic wave scattering. Zbl 0883.65098Yang, B.; Gottlieb, D.; Hesthaven, J. S. 20 1997 The resolution of the Gibbs phenomenon for “spliced” functions in one and two dimensions. Zbl 0911.65145Gelb, A.; Gottlieb, D. 16 1997 Spectral methods on arbitrary grids. Zbl 0862.65054Carpenter, Mark H.; Gottlieb, David 62 1996 A stable penalty method for the compressible Navier-Stokes equations. I: Open boundary conditions. Zbl 0853.76061Hesthaven, J. S.; Gottlieb, D. 55 1996 On the Gibbs phenomenon. III: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function. Zbl 0852.42017Gottlieb, David; Shu, Chi-Wang 23 1996 On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations. Zbl 0858.65096Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H. 22 1996 On the superconvergence of Galerkin methods for hyperbolic IBVP. Zbl 0858.65094Gottlieb, David; Gustafsson, Bertil; Olsson, Pelle; Strand, Bo 4 1996 The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A study of the boundary error. Zbl 0839.65098Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun 63 1995 On the Gibbs phenomenon. IV: Recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function. Zbl 0852.42018Gottlieb, David; Shu, Chi-Wang 33 1995 On the Gibbs phenomenon. V: Recovering exponential accuracy from collocation point values of a piecewise analytic function. Zbl 0852.42019Gottlieb, David; Shu, Chi-Wang 24 1995 A nonlinear Galerkin method: The two-level Fourier-collocation case. Zbl 0859.65111Dettori, Lucia; Gottlieb, David; Temam, Roger 6 1995 Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. Zbl 0832.65098Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul 216 1994 The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points. Zbl 0815.65106Don, Wai Sun; Gottlieb, David 34 1994 Resolution properties of the Fourier method for discontinuous waves. Zbl 0831.65016Gottlieb, David; Shu, Chi-Wang 10 1994 The stability of numerical boundary treatments for compact high-order finite-difference schemes. Zbl 0791.76052Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul 117 1993 Stable and accurate boundary treatments for compact, high-order finite- difference schemes. Zbl 0778.65057Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul 26 1993 Implementation of the nonlinear Galerkin method with pseudospectral (collocation) discretizations. Zbl 0782.65122Gottlieb, David; Temam, Roger 3 1993 On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function. Zbl 0781.42022Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Hervé 70 1992 On one-sided filters for spectral Fourier approximations of discontinuous functions. Zbl 0755.65140Cai, Wei; Gottlieb, David; Shu, Chi-Wang 8 1992 Cell averaging Chebyshev methods for hyperbolic problems. Zbl 0764.65056Cai, Wei; Gottlieb, David; Harten, Ami 6 1992 Convergence results for pseudospectral approximations of hyperbolic systems by a penalty-type boundary treatment. Zbl 0736.65074Funaro, Daniele; Gottlieb, David 23 1991 Secondary frequencies in the wake of a circular cylinder with vortex shedding. Zbl 0721.76069Abarbanel, Saul S.; Don, Wai Sun; Gottlieb, David; Rudy, David H.; Townsend, James C. 13 1991 The CFL condition for spectral approximations to hyperbolic initial- boundary value problems. Zbl 0723.65079Gottlieb, David; Tadmor, Eitan 11 1991 Spectral simulations of an unsteady compressible flow past a circular cylinder. Zbl 0722.76047Don, Wai-Sun; Gottlieb, David 9 1990 Quadrature imposition of compatibility conditions in Chebyshev methods. Zbl 0725.76060Gottlieb, D.; Streett, C. L. 1 1990 Essentially nonoscillatory spectral Fourier methods for shock wave calculations. Zbl 0666.65067Cai, Wei; Gottlieb, David; Shu, Chi-Wang 32 1989 An adaptive pseudo-spectral method for reaction diffusion problems. Zbl 0668.65092Bayliss, A.; Gottlieb, D.; Matkowsky, B. J.; Minkoff, M. 18 1989 Splitting methods for low Mach number Euler and Navier-Stokes equations. Zbl 0664.76088Abarbanel, Saul; Duth, Pravir; Gottlieb, David 13 1989 A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations. Zbl 0699.65079Funaro, D.; Gottlieb, D. 48 1988 Stability analysis of spectral methods for hyperbolic initial-boundary value systems. Zbl 0755.65099Gottlieb, David; Lustman, Liviu; Tadmor, Eitan 2 1988 Convergence of spectral methods for hyperbolic initial-boundary value systems. Zbl 0755.65098Gottlieb, David; Lustman, Liviu; Tadmor, Eitan 2 1988 Stability analysis of spectral methods for hyperbolic initial-boundary value systems. Zbl 0628.65109Gottlieb, David; Lustman, Liviu; Tadmor, Eitan 5 1987 Convergence of spectral methods for hyperbolic initial-boundary value systems. Zbl 0622.65110Gottlieb, David; Lustman, Liviu; Tadmor, Eitan 4 1987 Spectral methods for discontinuous problems. Zbl 0646.76082Abarbanel, S.; Gottlieb, D.; Tadmor, E. 14 1986 Multiple steady states for characteristic initial value problems. Zbl 0617.76079Salas, M. D.; Abarbanel, S.; Gottlieb, D. 12 1986 Improving the convergence rate to steady state of parabolic ADI methods. Zbl 0608.65055Abarbanel, Saul S.; Dwoyer, Douglas L.; Gottlieb, David 4 1986 Recovering pointwise values of discontinuous data within spectral accuracy. Zbl 0597.65099Gottlieb, David; Tadmor, Eitan 38 1985 Topics in spectral methods. Zbl 0564.65074Gottlieb, David; Turkel, Eli 9 1985 Spectral methods for compressible flow problems. Zbl 0554.76058Gottlieb, David 5 1985 Information content in spectral calculations. Zbl 0642.76085Abarbanel, Saul; Gottlieb, David 4 1985 Theory and applications of spectral methods. Zbl 0599.65079Gottlieb, David; Hussaini, M. Yousuff; Orszag, Steven A. 91 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 0534.00017Voigt, Robert G. (ed.); Gottlieb, David (ed.); Hussaini, M. Yousuff (ed.) 32 1984 Spectral methods for two-dimensional shocks. Zbl 0567.76068Gottlieb, David; Lustman, Liviu; Streett, Craig 5 1984 The spectrum of the Chebyshev collocation operator for the heat equation. Zbl 0537.65085Gottlieb, David; Lustman, Liviu 50 1983 The DuFort-Frankel Chebyshev method for parabolic initial boundary value problems. Zbl 0511.76003Gottlieb, David; Lustman, Liviu 6 1983 On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods. Zbl 0481.65072Gottlieb, David; Gunzburger, Max; Turkel, Eli 20 1982 Spectral computations of one dimensional inviscid compressible flows. Zbl 0561.76076Gottlieb, D.; Lustman, L.; Orszag, S. A. 78 1981 Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives. Zbl 0467.76062Abarbanel, Saul; Gottlieb, David 49 1981 The stability of pseudospectral-Chebyshev methods. Zbl 0469.65076Gottlieb, David 26 1981 Stability of pseudospectral and finite-difference methods for variable coefficient problems. Zbl 0537.65084Gottlieb, David; Orszag, Steven A.; Turkel, Eli 12 1981 On time discretizations for spectral methods. Zbl 0453.65059Gottlieb, David; Turkel, Eli 8 1980 High resolution spectral calculations of inviscid compressible flows. Zbl 0434.35067Orszag, Steven A.; Gottlieb, David 2 1980 Stability of two-dimensional initial boundary value problems using Leap- Frog type schemes. Zbl 0447.65055Abarbanel, Saul; Gottlieb, David 3 1979 Boundary conditions for multistep finite-difference methods for time- dependent equations. Zbl 0388.65039Gottlieb, David; Turkel, Eli 12 1978 Numerical analysis of spectral methods: Theory and applications. Zbl 0412.65058Gottlieb, David; Orszag, Steven A. 931 1977 Dissipative two-four methods for time-dependent problems. Zbl 0358.65074Gottlieb, David; Turkel, Eli 29 1976 Generalized DuFort-Frankel methods for parabolic initial-boundary value problems. Zbl 0344.35048Gottlieb, David; Gustafsson, Bertil 5 1976 Multidimensional difference schemes with fourth-order accuracy. Zbl 0328.65045Turkel, E.; Abarbanel, A.; Gottlieb, D. 5 1976 A note on the leap-frog scheme in two and three dimensions. Zbl 0331.65057Abarbanel, Saul; Gottlieb, David 4 1976 On the Navier-Stokes equations with constant total temperature. Zbl 0342.76025Gottlieb, David; Gustafsson, Bertil 2 1976 Difference schemes with fourth order accuracy for hyperbolic equations. Zbl 0325.65041Abarbanel, S.; Gottlieb, D.; Turkel, E. 9 1975 Hille-Wintner type oscillation criteria for linear ordinary differential equations of second order. Zbl 0313.34027Breuer, Shlomo; Gottlieb, David 3 1975 On proving stability of multidimensional difference schemes. Zbl 0312.65067Abarbanel, S.; Gottlieb, D. 3 1975 Phase error and stability of second order methods for hyperbolic problems. II. Zbl 0284.65078Gottlieb, David; Turkel, Eli 2 1974 Higher order accuracy finite difference algorithms for quasi-linear, conservation law hyperbolic systems. Zbl 0293.65072Abarbanel, S.; Gottlieb, D. 2 1973 ...and 8 more Documents all cited Publications top 5 cited Publications 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 all top 5 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. 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