List of publications [by subject classification]
Other lists of publications: [by chronological order] [selected publications] [significant publications]






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Reviews, Chapters in Books and Books

  • E. Tadmor
    Entropy stable schemes
    Handbook of Numerical Methods for Hyperbolic problems. Part A to appear.
  • E. Tadmor
    A review of numerical methods for nonlinear partial differential equations
    Bull. AMS, 49(4) (2012) 507-554.
  • E. Tadmor
    Selected topics in approximate solutions of nonlinear conservation laws. High-resolution central schemes
    ``Nonlinear Conservation Laws and Applications'' (A. Bressan, G-Q. Chen, M. Lewicka and D. Wang, eds), IMA Volumes in Mathematics and its Applications #153, Springer NY, (2011), pp. 101-122.
  • B. Cheng & E. Tadmor
    Approximate periodic solutions for the rapidly rotating shallow-water and related equations
    ``Water Waves. Theory and Experiment'', Proceedings of the Conference held in Howard University, May 2008 (M. F. Mahmood, D. Henderson, H. Segur, eds), World Scientific (2010), pp. 69-78.
  • E.Tadmor, J.-G. Liu & A. Tzavaras [AMS online catalogue] [Table of content ]
    Hyperbolic Problems: Theory, Numerics, Applications
    Proceedings of the Twelfth International Conference on Hyperbolic Problems held at the University of Maryland, College Park, June 9-13, 2008, AMS Proc. Symp. Appl. Math., 2009
    Vol. 67.1: Plenary & Invited Talks, ISBN: 978-0-8218-4729-9
    Vol. 67.2: Contributed Talks, ISBN: 978-0-8218-4730-5.
  • E. Tadmor & W. Zhong
    Energy-preserving and stable approximations for the two-dimensional shallow water equations
    ``Mathematics and Computation - A Contemporary View", Proceedings of the third Abel Symposium held in Ålesund Norway May 2006 (H. Munthe-Kaas and B. Owren eds.), Abel Symposia 3, Springer (2008) 67-94.
  • E. Tadmor
    Filters, mollifiers and the computation of the Gibbs phenomenon
    Acta Numerica v. 16 (2007) 305-378.
  • E. Tadmor
    Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems
    Acta Numerica v. 12 (2003), 451-512.

  • T. Hou & E. Tadmor [Springer online catalogue] [Table of content]
    Hyperbolic Problems: Theory, Numerics, Applications
    Proceedings of the Ninth International Conference on Hyperbolic Problems held in CalTech, Pasadena, March 25-29, 2002, Springer-Verlag (2003) ISBN: 3-540-44333-9.
  • E. Tadmor
    High resolution methods for time dependent problems with piecewise smooth solutions
    "International Congress of Mathematicians", Proceedings of the ICM02 Beijing 2002 (Li Tatsien, ed.), Vol. III: Invited lectures, Higher Education Press, (2002) 747-757.
  • E. Tadmor
    Approximate solution of nonlinear conservation laws and related equations
    ``Recent Advances in Partial Differential Equations and Applications" Proceedings of the 1996 Venice Conference in honor of Peter D. Lax and Louis Nirenberg on their 70th Birthday (R. Spigler and S. Venakides eds.), AMS Proceedings of Symposia in Applied Mathematics, 54 (1998) 325-368.
  • E. Tadmor [html file]
    Approximate solutions of nonlinear conservation laws
    ``Advanced Numerical Approximation of Nonlinear Hyperbolic Equations" C.I.M.E. course in Cetraro, Italy, June 1997 (A. Quarteroni ed.), Lecture notes in Mathematics 1697, Springer Verlag (1998) 1-149.
  • E. Tadmor
    Spectral methods for hyperbolic problems
    ``Methodes numeriques d'ordre eleve pour les ondes en regime transitoire", Lecture notes delivered at Ecole des Ondes, INRIA - Rocquencourt, January 24-28 (1994).
  • E. Tadmor
    Super viscosity and spectral approximations of nonlinear conservation laws
    ``Numerical Methods for Fluid Dynamics IV", Proceedings of the 1992 Conference on Numerical Methods for Fluid Dynamics, (M. J. Baines and K. W. Morton, eds.), Clarendon Press, Oxford (1993) 69-82.
  • E. Tadmor
    Stability analysis of finite-difference, pseudospectral and Fourier-Galerkin approximations for time-dependent problems
    SIAM Review 29 (1987), 525-555.
  • D. Gottlieb & E. Tadmor [MR 90a:65041]
    Recovering pointwise values of discontinuous data within spectral accuracy
    ``Progress and Supercomputing in Computational Fluid Dynamics", Proceedings of a 1984 U.S.-Israel Workshop, Progress in Scientific Computing, Vol. 6 (E. M. Murman and S. S. Abarbanel, eds.), Birkhauser, Boston (1985), 357-375.

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Stability of Runge-Kutta schemes

  • E. Tadmor
    From semi-discrete to fully discrete: stability of Runge-Kutta schemes by the energy method. II
    ``Collected Lectures on the Preservation of Stability under Discretization'', Lecture Notes from Colorado State University Conference, Fort Collins, CO, 2001 (D. Estep and S. Tavener, eds.) Proceedings in Applied Mathematics 109, SIAM 2002, 25-49.
  • S. Gottlieb, C.-W. Shu & E. Tadmor
    Strong stability-preserving high order time discretization methods
    SIAM Review 43 (2001) 89-112.
  • D. Levy & E. Tadmor
    From semi-discrete to fully-discrete: stability of Runge-Kutta schemes by the energy method
    SIAM Review 40 (1998) 40-73.

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Stability of difference and spectral approximations for initial value problems

  • E. Tadmor
    Spectral methods for hyperbolic problems
    "Methodes numeriques d'ordre eleve pour les ondes en regime transitoire", Lecture notes delivered at Ecole des Ondes, Inria - Rocquencourt January 24-28 (1994).
  • E. Tadmor
    Stability analysis of finite-difference, pseudospectral and Fourier-Galerkin approximations for time-dependent problems
    SIAM Review 29 (1987), 525-555.

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Stability of difference approximations for initial-boundary value problems

  • M. Goldberg E. Tadmor
    Simple stability criteria for difference approximations of hyperbolic initial-boundary value problems
    ``Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications", Proceedings of the 2nd International Conference on Nonlinear Hyperbolic Problems, Notes on Numerical Fluid Mechanics, Vol. 24 (J. Ballmann and R. Jeltsch eds.), Vieweg Verlag (1988), 179-185.
  • M. Goldberg & E. Tadmor
    Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems. II
    Mathematics of Computation 48 (1987), 503-520.

  • M. Goldberg & E. Tadmor [MR 87b:65144]
    New stability criteria for difference approximations of hyperbolic initial-boundary value problems
    ``Large-Scale Computations in Fluid Mechanics", Proceedings of the 15th AMS-SIAM Summer Seminar on Applied Mathematics held in Script Institute, San Diego, July 1983, Lectures in Applied Mathematics, Vol. 22-Part 1 (B. E. Engquist, S. Osher, and R. C. J. Somerville, eds.), American Mathematical Society, Rhode Island, (1985), 177-192.
  • M. Goldberg & E. Tadmor
    Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems
    Mathematics of Computation 44 (1985), 361-377.
  • E. Tadmor
    The unconditional instability of inflow-dependent boundary conditions in difference approximations to hyperbolic systems
    Mathematics of Computation 41 (1983), 309-319.

  • E. Tadmor
    The unconditional instability of inflow-dependent boundary conditions in difference approximations to hyperbolic systems
    ``Numerical Boundary Condition Procedures", Proceedings of the 1981 NASA Ames Research Center Symposium on Numerical Boundary Condition Procedures (P. Kutler, ed.), NASA Ames (1982) 323-332.
  • M. Goldberg & E. Tadmor
    Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II
    Mathematics of Computation 36 (1981), 603-626.
  • M. Goldberg & E. Tadmor
    Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I
    Mathematics of Computation 32 (1978), 1097-1107.

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Hyperbolic problems. Systems with different time scales

  • E.Tadmor, J.-G. Liu & A. Tzavaras [AMS online catalogue] [Table of content]
    Hyperbolic Problems: Theory, Numerics, Applications
    Proceedings of the Twelfth International Conference on Hyperbolic Problems held at the University of Maryland, College Park, June 9-13, 2008, AMS Proc. Symp. Appl. Math. (2009)
    Vol. 67.1: Plenary & Invited Talks, ISBN: 978-0-8218-4729-9
    Vol. 67.2: Contributed Talks, ISBN: 978-0-8218-4730-5.

  • T. Hou & E. Tadmor [Springer online catalogue] [Table of content]
    Hyperbolic Problems: Theory, Numerics, Applications
    Proceedings of the Ninth International Conference on Hyperbolic Problems held in CalTech, Pasadena, March 25-29, 2002, Springer-Verlag (2003) ISBN: 3-540-44333-9.
  • E. Tadmor
    Hyperbolic systems with different time scales
    Communications on Pure and Applied Mathematics 35 (1982), 839-866.
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Convection diffusion problems. Regularity and homogenization

  • S. He & E. Tadmor
    Suppressing chemotactic blow-up through a fast splitting scenario on the plane
    ArXiv:1710.06585
  • A. Biswas & E. Tadmor
    Dissipation versus quadratic nonlinearity: from a priori energy bound to higher-order regularizing effect
    Nonlinearity 27 (2014) 545-562.
  • E. Tadmor
    Burgers' equation with vanishing hyper-viscosity
    Communications in Math. Sciences 2 (2), (2004) 317-324.
  • E. Tadmor & T. Tassa
    On the homogenization of oscillatory solutions to scalar convection-diffusion equations
    Advances in Mathematical Sciences and Applications 7(1) (1997), 93-117.
  • E. Tadmor
    The well-posedness of the Kuramoto-Sivashinsky equation
    SIAM Journal on Mathematical Analysis 17 (1986), 884-893.

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Incompressible Euler, Navier-Stokes and related equations

  • H. Bae, A. Biswas & E. Tadmor
    Analyticity and decay estimates of the Navier-Stokes equations in critical Besov spaces
    Archive for Rational Mechanics and Analysis 205 (2012), 963-991.

  • E. Tadmor
    On a new scale of regularity spaces with applications to Euler's equations
    Nonlinearity 14 (2001), 513-532.
  • M. Lopes Filho, H. J. Nussenzveig & E. Tadmor
    Approximate solutions of the incompressible Euler equations with no concentrations
    Annales De L'institut Henri Poincare (c) Non Linear Analysis 17 (2000), 371-412.

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Critical threshold phenomena in Eulerian dynamics

  • D. Wei, E. Tadmor & H. Bae
    Critical thresholds in multi-dimensional Euler-Poisson equations with radial symmetry
    Communications in Mathematical Sciences 10(1) (2012), 75-86.

  • H. Liu, E. Tadmor & D. Wei
    Global regularity of the 4D Restricted Euler Equations
    Physica D 239 (2010) 1225-1231.
  • B. Cheng & E. Tadmor
    An improved local blow-up condition for Euler-Poisson equations with attractive forcing
    Physica D 238 (2009) 2062-2066.
  • D. Chae & E. Tadmor
    On the finite time blow-up of the Euler-Poisson equations in Rn
    Communications in Mathematical Sceinces 6(3) (2008) 785-789.
  • B. Cheng & E. Tadmor
    Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations
    SIAM Journal on Mathematical Analysis 39(5) (2008) 1668-1685.
  • E. Tadmor & D. Wei
    On the global regularity of sub-critical Euler-Poisson equations with pressure
    Journal of the European Mathematical Society 10 (2008) 757-769.
  • H. Liu & E. Tadmor
    Rotation prevents finite-time breakdown
    Physica D 188 (2004) 262-276.
  • H. Liu & E. Tadmor
    Critical thresholds and conditional stability for Euler equations and related models
    ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 9th International Conference in Pasadena, Mar. 2002 (T. Hou and E. Tadmor, eds.), Springer (2003) 227-240.
  • H. Liu & E. Tadmor
    Critical thresholds in 2D restricted Euler-Poisson equations
    SIAM Journal of Applied Mathematics63 (2003) 1889-1910.
  • H. Liu & E. Tadmor
    Semi-classical limit of the nonlinear Schrödinger-Poisson equation with sub-critical initial data
    Methods and Applications in Analysis 9(4) (2002), 517-532.
  • H. Liu & E. Tadmor
    Spectral dynamics of the velocity gradient field in restricted flows
    Communications in Mathematical Physics 228 (2002), 435-466.
  • H. Liu & E. Tadmor
    Critical thresholds in a convolution model for nonlinear conservation laws
    SIAM Journal on Mathematical Analysis 33 (2001), 930-945.
  • S. Engelberg, H. Liu & E. Tadmor
    Critical thresholds in Euler-Poisson equations
    Indiana University Math journal  50 (2001), 109-157..
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Nonlinear conservation laws. Entropy and regularity

  • K. Karlsen, M. Rascle & E. Tadmor
    On the existence and compactness of a two-dimensional resonant system of conservation laws
    Communications in Mathematical Sciences 5(2) (2007) 253-265.

  • E. Tadmor, M. Rascle & P. Bagnerini
    Compensated compactness for 2D conservation laws
    Journal of Hyperbolic Differential Equations 2(3) (2005) 697-712.
  • E. Tadmor & T. Tassa
    On the piecewise regularity of entropy solutions to scalar conservation laws
    Communications on Partial Differential Equations 18 (1993), 1631-1652.
  • E. Tadmor
    Entropy functions for symmetric systems of conservation laws
    Journal of Mathematical Analysis and Applications 122(2) (1987), 355-359.
  • E. Tadmor
    A minimum entropy principle in the gas dynamics equations
    Applied Numerical Mathematics 2 (1986), 211-219.

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Self-organized dynamics and hydrodynamics flocking

  • R. Shvydkoy & E. Tadmor
    Eulerian dynamics with a commutator forcing III: Fractional diffusion of order 0<α<1
    Physica D accepted, arXiv:1706.08246
  • R. Shvydkoy & E. Tadmor
    Eulerian dynamics with a commutator forcing II: flocking
    Discrete and Continuous Dynamical Systems-A 37(11) (2017) 5503-5520.
  • S. He & E. Tadmor
    Global regularity of two-dimensional flocking hydrodynamics
    Comptes rendus - Mathématique Ser. I 355 (2017) 795–805.
  • R. Shvydkoy & E. Tadmor
    Eulerian dynamics with a commutator forcing
    Transactions of Mathematics and its Applications 1(1) (2017) 1-26.
  • J. A. Carrillo, Y.-P. Choi E. Tadmor & C. Tan
    Critical thresholds in 1D Euler equations with nonlocal forces
    Mathematical Models and Methods in Applied Sciences 26(1) (2016) 185-206.
  • E. Tadmor
    Mathematical aspects of self-organized dynamics:
    consensus, emergence of leaders, and social hydrodynamics

    SIAM News 48(9) 2015.
  • C. Tan & E. Tadmor
    Critical thresholds in flocking hydrodynamics with nonlocal alignment
    Proceedings of the Royal Society A 372:20130401 (2014).
  • S. Motsch & E. Tadmor
    Heterophilious dynamics enhances consensus
    SIAM Review 56(4) (2014) 577–621.
  • S. Motsch & E. Tadmor
    A new model for self-organized dynamics and its flocking behavior
    Journal of Statistical Physics 144(5) (2011) 923-947.
  • S.-Y. Ha & E. Tadmor
    From particle to kinetic and hydrodynamic descriptions of flocking
    Kinetic and Related Models 1(3) (2008) 415-435.

Kinetic formulations of nonlinear conservation laws and related equations

  • E. Tadmor & T. Tao
    Velocity averaging, kinetic formulations and regularizing effects in quasilinear PDEs
    Communications on Pure & Applied Mathematics 60 (2007), 1488-1521.
  • P.-L. Lions, P. Perthame & E. Tadmor
    Kinetic formulation of the isentropic gas dynamics and p-systems
    Communications in Mathematical Physics 163 (1994), 415-431.
  • P.-L. Lions, P. Perthame & E. Tadmor
    A kinetic formulation of multidimensional scalar conservation laws and related equations
    Journal of the American Mathematical Society 7 (1994), 169-191.
  • S. Schochet & E. Tadmor
    Regularized Chapman-Enskog expansion for scalar conservation laws
    Archive for Rational Mechanics and Analysis 119 (1992), 95-107.

  • P.-L. Lions, B. Perthame & E. Tadmor [MR 91k:35156]
    Formulation cinétique des lois de conservation scalaires multidimensionelles
    Comptes Rendus de l'Académie des Sciences, Paris, Série I (1991), 97-102.
  • B. Perthame & E. Tadmor
    A kinetic equation with kinetic entropy functions for scalar conservation Laws
    Communications in Mathematical Physics, 136 (1991), 501-517.

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Approximate methods for nonlinear PDEs. Reviews

  • E. Tadmor
    Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems
    Acta Numerica v. 12 (2003), 451-512.
  • E. Tadmor
    High resolution methods for time dependent problems with piecewise smooth solutions
    ``International Congress of Mathematicians", Proceedings of the ICM02 Beijing 2002 (Li Tatsien, ed.), Vol. III: Invited lectures, Higher Education Press (2002) 747-757.
  • E. Tadmor [html file]
    Approximate solutions of nonlinear conservation laws
    ``Advanced Numerical Approximation of Nonlinear Hyperbolic Equations", C.I.M.E. course in Cetraro, Italy, June 1997 (A. Quarteroni ed.), Lecture notes in Mathematics 1697, Springer Verlag (1998) 1-149.
  • E. Tadmor
    Approximate solution of nonlinear conservation laws and related equations
    ``Recent Advances in Partial Differential Equations and Applications" Proceedings of the 1996 Venice Conference in honor of Peter D. Lax and Louis Nirenberg on their 70th Birthday (R. Spigler and S. Venakides eds.), AMS Proceedings of Symposia in Applied Mathematics 54 (1998) 325-368.

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Finite difference approximations. Total-variation and entropy stability

  • U. Fjordholm, R. Kappeli, S. Mishra & E. Tadmor
    Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws
    Foundations of Computational Mathematics 17 (2017) 763–827.
  • E. Tadmor
    Entropy stable schemes
    Handbook of Numerical Methods for Hyperbolic problems. Vol. XVII (R. Abgrall and C.-W. Shu, eds), Elsevier (2016) pp. 467-493.
  • U. Fjordholm, S. Mishra & E. Tadmor
    On the computation of measure-valued solutions
    Acta Numerica 25 (2016) 567-679.
  • E. Tadmor
    Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws
    Discrete and Continuous Dynamical Systems-A 36(8) (2016) 4579-4598.
  • U. Fjordholm, S. Mishra & E. Tadmor
    Entropy stable ENO scheme
    ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 13th International Conference held in Beijing, June 2010 (T. Li & S. Jiang, eds.), vol 1, Contemporary Appl. Math. 17, Higher Ed. Press (2012) 12-27.
  • U. Fjordholm, S. Mishra & E. Tadmor
    ENO reconstruction and ENO interpolation are stable(+errata)
    Foundations of Computational Mathematics 13(2) (2012), 139-159.
  • U. Fjordholm, S. Mishra & E. Tadmor
    Arbitrarily high order accurate entropy stable essentially non-oscillatory schemes for systems of conservation laws
    SIAM Jounral on Numerical Analysis 50(2), (2012) 544-573.
  • U. Fjordholm, S. Mishra & E. Tadmor
    Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography
    Journal of Computational Physics 230 (2011), 5587-5609.
  • M. Lukacova - Medvidova & E. Tadmor
    On the entropy stability of Roe-type finite volume methods
    ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 12th International Conference held in University of Maryland, June 2008 (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied Math., 67(2) (2009) 765-774.
  • A. Madrane & E. Tadmor
    Entropy stability of Roe-type upwind finite volume methods on unstructured grids
    ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 12th International Conference held in University of Maryland, June 2008 (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied Math., 67(2) (2009) 775-784.
  • U. Fjordholm, S. Mishra & E. Tadmor
    Energy preserving and energy stable schemes for the shallow water equations
    ``Foundations of Computational Mathematics", Proceedings of FoCM held in Hong Kong 2008 (F. Cucker, A. Pinkus & M. Todd, eds), London Math. Soc. Lecture Notes Ser. 363, (2009) 93-139.
  • E. Tadmor & W. Zhong
    Energy-preserving and stable approximations for the two-dimensional shallow water equations
    ``Mathematics and Computation - A Contemporary View", Proceedings of the Third Abel Symposium held in Ålesund, Norway May 2006 (H. Munthe-Kaas & B. Owren eds.), Springer (2008) 67-94.
  • E. Tadmor & W. Zhong
    Novel entropy stable schemes for 1D and 2D fluid equations
    ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 11th International Conference in Lyon, July 2006 (S. Benzoni-Gavage and D. Serre, eds.), Springer (2007) 1111-1120.
  • E. Tadmor & W. Zhong
    Entropy stable approximations of Navier-Stokes equations with no artificial numerical viscosity
    J. of Hyperbolic Differential Equations 3(3) (2006) 529-559.
  • E. Tadmor
    On the entropy stability of difference schemes: a comparison principle and a homotopy approach
    ``Hyperbolic Problems: Theory, Numerics, Applications'', vol. I., Proceedings of the 10th International Conference, Osaka, Sep. 2004 (F. Asukura, H. Aiso, S. Kawashima, A. Matsumura, S. Nishibata & K. Nishihara, eds.), Yokohama Publishers, (2006) 195-204.
  • E. Tadmor
    Convenient total variation diminishing conditions for nonlinear difference schemes
    SIAM Journal on Numerical Analysis 25 (1988), 1002-1014.
  • S. Osher & E. Tadmor
    On the convergence of difference approximations to scalar conservation laws
    Mathematics of Computation 50 (1988), 19-51.
  • E. Tadmor
    The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes
    ``Nonlinear Hyperbolic Problems'', Proceedings of a 1986 Advanced Research Workshop, Lecture Notes in Mathematics, Vol. 1270 (C. Carasso, P.-A. Raviart and D. Serre, eds.), Springer-Verlag, 1987, pp. 52-63.
  • E. Tadmor
    The numerical viscosity of entropy stable schemes for systems of conservation laws. I.
    Mathematics of Computation 49 (1987), 91-103
    [consult NASA Langley Report: "CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences" (references [87],[88])]
  • E. Tadmor
    Entropy conservative finite element schemes
    ``Numerical Methods for Compressible Flows - Finite Difference Element and Volume Techniques", Proceedings of the winter annual meeting of the American Society of Mechanical Engineering (T. E. Tezduyar and T.J.R. Hughes, eds.), AMD-Vol. 78 (1986), 149-158.
  • E. Tadmor
    Skew self-adjoint form for systems of conservation laws
    Journal of Mathematical Analysis and Applications 103(2) (1984) 428-442.
  • E. Tadmor
    Numerical viscosity and the entropy condition for conservative difference schemes
    Mathematics of Computation 43 (1984), 369-381.
  • E. Tadmor
    The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme
    Mathematics of Computation 43 (1984), 353-368.

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Potential-based approximations of constraint transport equations

  • S. Mishra & E. Tadmor
    Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for the MHD equations
    Mathematical Modeling and Numerical Analysis 46 (2012) 661-680.

  • S. Mishra & E. Tadmor
    Constraint preserving schemes using potential-based fluxes. II. Genuinely multi-dimensional systems of conservation laws
    SIAM Journal on Numerical Analysis 49(3) (2011) 1023-1045.

  • S. Mishra & E. Tadmor
    Constraint preserving schemes using potential-based fluxes. I. Multidimensional transport equations
    Communications in Computational Physics 9(3) (2010) 688-710.

  • S. Mishra & E. Tadmor
    Potential-based, constraint preserving, genuinely multi-dimensional schemes for systems of conservation laws
    ``Nonlinear Partial Differenetial Equations'', Proceedings of the 2008-2009 Special Year in Nonlinear PDEs held in Center Advanced Study, Oslo (H. Holden & K. Karlsen, eds.), AMS Contemporary Mathematics 526 (2010), 295-314.
  • S. Mishra & E. Tadmor
    Vorticity preserving schemes using potential-based fluxes for the system wave equation
    ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 12th International Conference held in University of Maryland, June 2008 (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied Math., 67(2) (2009) 795-804
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Approximation of nonlinear conservation laws. Convergence rate estimates

  • E. Tadmor & T. Tang
    Pointwise error estimates for relaxation approximations to conservation laws
    SIAM Journal on Mathematical Analysis 32 (2001), 870-886.
  • C.-T. Lin & E. Tadmor
    L1-stability and error estimates for approximate Hamilton-Jacobi solutions
    Numerische Mathematik 87 (2001) 701-735.
  • E. Tadmor & T. Tang
    Pointwise convergence rate for nonlinear conservation laws
    ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 7 th International Conference in Zurich, Feb. 1998 (M. Fey and R. Jeltsch, eds.), Int'l Series Numer. Math., Vol. 130, Birkhauser (1999) 925-934.
  • E. Tadmor & T. Tang
    Pointwise error estimates for scalar conservation laws with piecewise smooth solutions
    SIAM Journal on Numerical Analysis 36 (1999) 1739-1756.
  • A. Kurganov & E. Tadmor
    Stiff systems of hyperbolic conservation laws: convergence and error estimates
    SIAM Journal on Mathematical Analysis, 28 (1997) 1446-1456.
  • H. Nessyahu, E. Tadmor & T. Tassa
    The convergence rate of Godunov type schemes
    SIAM Journal on Numerical Analysis, 31 (1994), 1-16.
  • H. Nessyahu & E. Tadmor
    The convergence rate of approximate solutions for nonlinear scalar conservation laws
    SIAM Journal on Numerical Analysis, 29 (1992), 1505-1519.
  • E. Tadmor
    Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
    SIAM Journal on Numerical Analysis, 28 (1991), 891-906.

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Non-oscillatory central schemes. I. Nonlinear conservation laws

  • H. Yousefi, E. tadmor & T. Rabczuk
    High resolution wavelet based central schemes for modeling nonlinear propagating fronts
    preprint.
  • A. Chertock, S. Cui, A. Kurganov, S.-N. Özcan & E. Tadmor
    Well-balanced schemes for the Euler equations with gravitation: conservative formulation using global fluxes
    preprint.
  • Y.-J. Liu, C.-W. Shu, E. Tadmor  & M. Zhang
    Central local discontinuous Galerkin methods on overlapping cells for diffusion equations
    Mathematical Modeling and Numerical Analysis 45 (2011) 1009-1032.
     
  • Y.-J. Liu, C.-W. Shu, E. Tadmor  & M. Zhang
    L2-stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
    Mathematical Modeling and Numerical Analysis 42 (2008) 593-607 [highlighted paper].
     
  • Y.-J. Liu, C.-W. Shu, E. Tadmor  & M. Zhang
    Non-Oscillatory hierarchical reconstruction for central and finite volume schemes
    Communications in Computational Physics 2(5) (2007) 933-963.
  • Y.-J. Liu, C.-W. Shu, E. Tadmor  & M. Zhang
    Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction
    SIAM Jounrnal on Numerical Analysis 45(6) (2007) 2442-2467.
  • J. Balbas & E. Tadmor 
    Non-oscillatory central schemes for one- and two-dimensional MHD equations. II: high-order semi-discrete schemes
    SIAM Journal on Scientific Computing 28 (2006) 533-560.
  • J. Balbas & E. Tadmor 
    A central differencing simulation of the Orszag-Tang vortex system
    IEEE Transactions on Plasma Science, The 4th Triennial Special Issue on Images in Plasma Science 33(2) (2005) 470-471.
  • J. Balbas, E. Tadmor, & C.-C. Wu  [Numerical simulations]
    Non-oscillatory central schemes for one- and two-dimensional MHD equations
    Journal of Computational Physics 201 (2004) 261-285.
     
  • A. Kurganov & E. Tadmor
    Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers
    Numerical Methods for Partial Differential Equations, 18 (2002) 548-608.
  • A. Kurganov & E. Tadmor
    New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
    Journal of Computational Physics, 160 (2000) 214-282.
  • G.-S. Jiang, D. Levy, C.-T. Lin, S. Osher & E. Tadmor
    High-resolution non-oscillatory central schemes with non-staggered grids for hyperbolic conservation laws
    SIAM Journal on Numerical Analysis, 35 (1998) 2147-2168.
  • D. Levy & E. Tadmor
    Non-oscillatory boundary treatment for staggered central schemes
  • G.-S. Jiang & E. Tadmor
    Non-oscillatory central schemes for multidimensional hyperbolic conservation laws
    SIAM Journal on Scientific Computing 19 (1998), 1892-1917.
  • X-D. Liu & E. Tadmor
    Third order nonoscillatory central scheme for hyperbolic conservation laws
    Numerische Mathematik 79 (1998), 397-425.
  • H. Nessyahu & E. Tadmor
    Non-oscillatory central differencing for hyperbolic conservation laws
    Journal of Computational Physics 87 (1990), 408-463.

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Non-oscillatory central schemes. II. Incompressible Euler equations

  • D. Levy & E. Tadmor, reprint with embedded figures: , preprint with original figures:
    Non-oscillatory central schemes for the incompressible 2-D Euler equations
    Mathematical Research Letters, 4(3) (1997) 321-340.

  • R. Kupferman & E. Tadmor
    A fast high-resolution second-order central scheme for incompressible flows
    Proceedings of the National Academy of Sciences 94 (1997) 4848-4852.

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Non-oscillatory central schemes. III. Hamilton-Jacobi equations

  • C.-T. Lin & E. Tadmor
    L1-stability and error estimates for approximate Hamilton-Jacobi solutions
    Numerische Mathematik 87 (2001) 701-735.
  • C.-T. Lin & E. Tadmor
    High-resolution non-oscillatory central scheme for Hamilton-Jacobi equations
    SIAM Journal on Scientific Computation 21 (2000) 2163-2186.
  • A. Kurganov & E. Tadmor
    New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations
    Journal of Computational Physics 160 (2000) 720-742.

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Spectral recovery and detection of edges in spectral data

  • E. Tadmor & J. Zou
    Novel edge detection methods for incomplete and noisy spectral data
    Journal of Fourier Analysis and Applications 14(5) (2008) 744-763.

  • S. Engelberg & E. Tadmor
    Recovery of edges from spectral data with noise---a new perspective
    SIAM Journal on Numerical Analysis 46(5) (2008) 2620-2635.
  • E. Tadmor
    Filters, mollifiers and the computation of the Gibbs phenomenon
    Acta Numerica 16 (2007) 305-378.
  • A. Gelb & E. Tadmor
    Adaptive edge detectors for piecewise smooth data based on the minmod limiter
    Journal of Scientific Computing 28(2-3) (2006) 279-306.
  • E. Tadmor & J. Tanner
    Adaptive filters for piecewise smooth spectral data
    IMA Journal of Numerical Analysis 25(4) (2005) 635-647.
  • E. Tadmor & J. Tanner
    An adaptive order Godunov type central scheme
    "Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 9th International Conference held in CalTech Pasadena, Mar. 2002 (T. Hou and E. Tadmor, eds.), Springer (2003) 871-880.
  • A. Gelb & E. Tadmor
    Spectral reconstruction of one- and two-dimensional piecewise smooth functions from their discrete data
    Mathematical Modeling and Numerical Analysis 36 (2002) 155-175.

  • E. Tadmor & J. Tanner
    Adaptive mollifiers -- high resolution recovery of piecewise smooth data from its spectral information
    Foundations of Computational Mathematics 2(2) (2002) 155-189.

  • A. Gelb & E. Tadmor
    Detection of edges in spectral data II. Nonlinear enhancement
    SIAM Journal on Mumerical Analysis 38 (2000), 1389-1408.

  • A. Gelb & E. Tadmor
    Detection of edges in spectral data
    Applied and Computational Harmonic Analysis 7 (1999) 101-135.

  • S. Abarbanel, D. Gottlieb & E. Tadmor
    Spectral methods for discontinuous problems
    "Numerical Methods for Fluid Dynamics II", Proceedings of the 1985 Conference on Numerical Methods for Fluid Dynamics (K. W. Morton and M. J. Baines, eds.), Clarendon Press, Oxford (1986), 129-153.
  • E. Tadmor
    The exponential accuracy of Fourier and Chebyshev differencing methods
    SIAM Journal on Numerical Analysis 23 (1986), 1-10.
  • D. Gottlieb & E. Tadmor [SIAM Rev 28(4) 1986] [MR 90a:65041]
    Recovering pointwise values of discontinuous data within spectral accuracy
    &qout;Progress and Supercomputing in Computational Fluid Dynamics", Proceedings of a 1984 U.S.-Israel Workshop, Progress in Scientific Computing, Vol. 6 (E. M. Murman and S. S. Abarbanel, eds.), Birkhauser, Boston (1985) 357-375.

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Stability and convergence of spectral methods

  • C. Bardos & E. Tadmor
    Stability and spectral convergence of Fourier method for nonlinear problems. On the shortcomings of the 2/3 de-aliasing method
    Numerische Mathematik 129 (2014) 749-782.

  • J. Goodman, T. Hou & E. Tadmor
    On the stability of the unsmoothed Fourier method for hyperbolic equations
    Numerische Mathematik 67(1) (1994), 93-129.

  • D. Gottlieb & E. Tadmor
    The CFL condition for spectral approximations to hyperbolic initial-boundary value problems
    Mathematics of Computation 56 (1991), 565-588.

  • E. Tadmor (1991)
    Essentially non-oscillatory spectral viscosity approximations
    "Hyperbolic Problems - Theory, Numerical Methods and Applications", Proceedings of the 3rd International Conference on Hyperbolic Problems, Vol. II (B. Engquist and B. Gustafsson, eds.), Studentlitteratur and Chartwell-Bratt (1991), 861-873.

  • D. Gottlieb, L. Lustman & E. Tadmor
    Convergence of spectral methods for hyperbolic initial-boundary value systems
    SIAM Journal on Numerical Analysis 24 (1987), 532-537.
  • D. Gottlieb, L. Lustman & E. Tadmor
    Stability analysis of spectral methods for hyperbolic initial-boundary value systems
    SIAM Journal on Numerical Analysis 24 (1987), 241-256.

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Spectral viscosity approximations

  • E. Tadmor & K. Waagan
    Adaptive spectral viscosity for hyperbolic conservation laws
    SIAM journal on Scientific Computation 34(2) (2012), 993-1009.

  • B.-Y. Guo, H.-P. Ma & E. Tadmor
    Spectral vanishing viscosity method for nonlinear conservation laws
    SIAM Journal on Numerical Analysis 39 (2001), 1254-1268.
  • A. Gelb & E. Tadmor
    Enhanced spectral viscosity approximations for conservation laws
    Applied Numerical Mathematics 33 (2000), 3-21.
  • G.-Q. Chen, Q. Du & E. Tadmor
    Spectral viscosity approximations to multidimensional scalar conservation laws
    Mathematics of Computation 61 (1993), 629-643.
  • E. Tadmor
    Super viscosity and spectral approximations of nonlinear conservation laws
    "Numerical Methods for Fluid Dynamics IV", Proceedings of the 1992 Conference on Numerical Methods for Fluid Dynamics, (M. J. Baines and K. W. Morton, eds.), Clarendon Press, Oxford (1993) 69-82.
  • E. Tadmor
    Total-variation and error estimates for spectral viscosity approximations
    Mathematics of Computation 60 (1993), 245-256.
  • Y. Maday, S. M. Ould Kaber & E. Tadmor
    Legendre pseudospectral viscosity method for nonlinear conservation laws
    SIAM Journal on Numerical Analysis 30 (1993), 321-342.
  • E. Tadmor [MR 92b:65076]
    Essentially non-oscillatory spectral viscosity approximations
    "Hyperbolic Problems - Theory, Numerical Methods and Applications", Proceedings of the 3rd International Conference on Hyperbolic Problems, Vol. II (B. Engquist and B. Gustafsson, eds.), Studentlitteratur and Chartwell-Bratt (1991) 861-873.
  • E. Tadmor
    Shock capturing by the spectral viscosity method
    ``Spectral and High Order Methods for Partial Differential Equations", Proceedings of the ICOSAHOM '89 Conference held in Como, Italy 1989 (C. Canuto and A. Quarteroni, eds), North-Holannd (1990) 197-208;
    Computer Methods in Applied Mechanics and Engineering 78 (1990), 197-208.
  • Y. Maday & E. Tadmor
    Analysis of the spectral vanishing viscosity method for periodic conservation laws
    SIAM Journal on Numerical analysis 26 (1989), 854-870.
  • E. Tadmor

    Convergence of the spectral viscosity method for nonlinear conservation laws
    "11th International Conference on Numerical Methods in Fluid Dynamics", Lecture Notes in Physics, Vol. 323 (D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt, eds.), Springer-Verlag (1989) 548-552.
  • E. Tadmor
    Convergence of spectral methods for nonlinear conservation laws
    SIAM Journal on Numerical Analysis 26 (1989), 30-44.

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Multiscale representations in imaging and PDEs

  • E. Tadmor
    Hierarchical construction of bounded solutions in critical regularity spaces
    Communications in Pure & Applied Mathematics 69(6) (2016) 1087-1109.
  • E. Tadmor & C. Tan
    Hierarchical construction of bounded solutions of div U=F in critical regularity spaces
    "Nonlinear Partial Differential Equations", Proceedings of the 2010 Abel Symposium held in Oslo, Sep. 2010 (H. Holden & K. Karlsen eds.), Abel Symposia 7, Springer 2011, 255-269.
  • P. Athavale & E. Tadmor
    Integro-differential equations based on (BV, L1) image decomposition
    SIAM journal on Imaging Sciences 4(1) (2011) 300-312.
  • P. Athavale & E. Tadmor
    Novel integro-differential equations in image processing and its applications
    "Computational Imaging VIII", Proceedings of SPIE meeting held Jan. 2010, San Jose (C. A. Bouman, I. Pollak, P. J. Wolfe eds.), vol. 7533, 75330S.
  • E. Tadmor & P. Athavale
    Multiscale image representation using integro-differential equations
    Inverse Problems and Imaging 3(4) (2009) 693-710.
  • E. Tadmor, S. Nezzar & L. Vese
    Multiscale hierarchical decomposition of images with applications to deblurring, denoising and segmentation
    Communications in Mathematical Sciences 6(2) (2008) 281-307.
  • E. Tadmor, S. Nezzar & L. Vese
    A multiscale image representation using hierarchical (BV,L2) decompositions
    Multiscale Modeling and Simulations 2(4) (2004) 554-579.

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Matrix theory -- the numerical radius, power-boundedness and eigen-solvers

  • D. Gill & E. Tadmor
    An O(N2) method for computing the eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach
    SIAM Journal on Scientific and Statistical Computing 11 (1990), 161-173.
  • D. Gill & E. Tadmor
    An O(N2) method for computing the eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach; Short communication
    Linear Algebra and its Applications 120, (1989), 257-258 .
  • E. Tadmor
    The resolvent condition and uniform power-boundedness
    "Haifa Conference on Matrix Theory", Report (A. Berman, Y. Censor and H. Schneider, eds.)
    Linear Algebra and Its Applications 80 (1986), 250-252.
  • E. Tadmor
    Complex symmetric matrices with strongly stable iterates
    Linear Algebra and Its Applications 78 (1986), 65-77.
  • S. Friedland & E. Tadmor
    Optimality of the Lax-Wendroff condition
    Linear Algebra and its Applications 56 (1984), 121-129.
  • M. Goldberg & E. Tadmor
    On the numerical radius and its applications
    Linear Algebra and its Applications 42 (1982), 263-284.
  • E. Tadmor
    The equivalence of L2-stability, the resolvent condition and strict H-stability
    Linear Algebra and its Applications 41 (1981), 151-159.
  • M. Goldberg, E. Tadmor & G. Zwas
    Numerical radius of positive matrices
    Linear Algebra and its Applications 12 (1975), 209-214.
  • M. Goldberg, E. Tadmor & G. Zwas
    The numerical radius and spectral matrices
    Linear and Multilinear Algebra 2 (1975), 317-326.



[Acknowledgement]