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LISTE DE PUBLICATIONS (suivie des prépublications)


  1. Max Duarte, Marc Massot, Stéphane Descombes, Parareal operator splitting techniques for multi-scale reaction waves : Numerical analysis and strategies , to appear in M2AN.

  2. S. Descombes, M. Thalhammer, An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime, BIT. Numerical Mathematics, 50, no. 4, p.729-749 (2010).

  3. P. Chartier, F. Castella, S. Descombes, G. Vilmart, Splitting methods with complex times for parabolic equations, BIT. Numerical Mathematics, 49, no. 3, p.487-508 (2009).

  4. M. A. Dronne, E. Grenier, S. Descombes, H. Gilquin, Examples of the influence of the geometry on the propagation of progressive waves, Math. Comput. Modelling, 49, no. 11-12, p.2138--2144 (2009).

  5. E. Grenier, M.A. Dronne, S. Descombes, H. Gilquin, A. Jaillard, M. Hommel, J.P. Boissel, A numerical study of the blocking of migraine by Rolando sulcus, Progress in Biophysics and Molecular Biology, 97 (1), p.54-59 (2008).

  6. S. Descombes, T. Dumont, Numerical simulation of a stroke: Computational problems and methodology, Progress in Biophysics and Molecular Biology, 97 (1), p.40-53, (2008).

  7. S. Descombes, T. Dumont, V. Louvet, M. Massot, On the local and global errors of splitting approximations of reaction-diffusion equations with high spatial gradients, International Journal of Computer Mathematics 84 (2007), no. 6, 749--765.

  8. S. Benzoni-Gavage, R. Danchin, S. Descombes, Well-posedness of one-dimensional Korteweg models, Electronic Journal of Differential Equations, 59 (2006), 1 - 35.

  9. S. Benzoni-Gavage, R. Danchin, S. Descombes, On the well-posedness of the Euler-Korteweg model in several space dimensions, Indiana University Mathematics Journal 56 (2007), no. 4, 1499–1579.

  10. X. Antoine, C. Besse, S. Descombes, Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations, SIAM J. Numer. Anal., 43 (2006), no. 6, 2272 - 2293.

  11. S. Benzoni-Gavage, R. Danchin, S. Descombes, D. Jamet, Structure of Korteweg models and stability of diffuse interfaces, Interfaces and Free Boundaries. Modelling, Analysis and Computation, 7 (2005), no. 4, 371--414.

  12. S. Descombes, M. Massot, Operator splitting for nonlinear reaction-diffusion systems with an entropic structure : singular perturbation and order reduction, Numerische Mathematik (2004) Volume 97, Number 4, pp. 667 - 698.

  13. A.B. Iskakov, S. Descombes, E. Dormy, An integro-differential formulation for magnetic induction in bounded domains: boundary element--finite volume method, J. Comput. Phys. 197 (2004), no. 2, pp. 540-554.

  14. S. Descombes, M. Ribot, Convergence of the Peaceman-Rachford approximation for reaction-diffusion systems, Numerische Mathematik (2003) Volume 95, Number 3, pp. 503 - 525.

  15. C. Besse, B. Bidégaray, S. Descombes, Order estimates in time of splitting methods for the nonlinear Schrödinger equation, SIAM J. Numer. Anal. 40 (2002), no. 5, 26--40.

  16. S. Descombes, M. Schatzman, Strang's formula for holomorphic semi-groups, J. Math. Pures Appl. 81 (2002), no. 1, 93--114

  17. S. Descombes, Convergence of a splitting method of high order for reaction-diffusion systems, Math. Comp. 70 (2001), no. 236, 1481--1501.

  18. S. Descombes, B. O. Dia, An operator theoretic proof of an estimate on the transfer operator, J. Funct. Anal. 165 (1999), no. 2, 240--257.

  19. S. Descombes, M. Moussaoui, Global existence and regularity of solutions for complex Ginzburg-Landau equations, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 3 (2000), no. 1, 193--211.

  20. S. Descombes, M. Schatzman, On Richardson Extrapolation of Strang's Formula for Reaction-Diffusion Equations, Equations aux Dérivées Partielles et Applications, articles dédiés à Jacques-Louis Lions, p. 429-452, Gauthier-Villars Elsevier, Paris, 1998.

  21. S. Descombes, M. Schatzman, Directions alternées d'ordre élevé en réaction-diffusion, C.R. Acad. Sci. Paris, t.321, Série I, p 1521-1524, 1995.

  22. S. Descombes, M. Moussaoui, Existence globale et régularité de solutions d'équations de Ginzburg-Landau complexes, C.R. Acad. Sci. Paris, t.329, Série I, p 189-192, 1999.


PROCEEDINGS


  1. S. Descombes, T. Dumont, M. Massot, Operator splitting for stiff nonlinear reaction-diffusion systems : order reduction and application to spiral waves,
    ``Patterns and waves'',
    A. Abramian, S. Vakulenko, V. Volpert (Eds),
    Saint-Petersbourg, 2003, pp. 386-402.

  2. S. Benzoni-Gavage, R. Danchin, S. Descombes, D. Jamet, On Korteweg models for fluids exhibiting phase changes,
    Proceedings of 10th International Conference on Hyperbolic Problems, Osaka (2004),
    Yokohama Publishers, Inc.

  3. S. Benzoni-Gavage, R. Danchin, S. Descombes, D. Jamet, Stability issues in the Euler-Korteweg model,
    à paraître dans Contemporary Mathematics, A.M.S. (2007).
    Proceedings of the Summer Research Conference on Control Methods in PDE-Dynamical Systems, Snowbird (2005).

  4. S. Descombes, V. Dolean, M. Gander, Schwarz Waveform Relaxation Methods for Systems of Semi-Linear Reaction-Diffusion Equations,
    Proceedings of the 19th International Conference on Domain Decomposition Methods, 2009.


PREPUBLICATIONS


  1. S. Descombes, M. Thalhammer, The Lie-Trotter splitting method for nonlinear evolutionary problems involving critical parameters. An exact local error representation and application to nonlinear Schrödinger equations in the semi-classical regime,

  2. Max Duarte, Marc Massot, Stéphane Descombes, Christian Tenaud, Thierry Dumont, Violaine Louvet, Frédérique Laurent, New resolution strategy for multi-scale reaction waves using time operator splitting, space adaptive multiresolution and dedicated high order implicit/explicit time integrators,

  3. Thierry Dumont, Max Duarte, Stéphane Descombes, Marie-Aimée Dronne, Marc Massot, Violaine Louvet, Simulation of human ischemic stroke in realistic 3D geometry : A numerical study,



Stéphane Descombes.
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