Free Access
Math. Model. Nat. Phenom.
Volume 8, Number 3, 2013
Front Propagation
Page(s) 182 - 197
Published online 12 June 2013
  1. M. Abel, M. Cencini, D. Vergni, A. Vulpiani. Front speed enhancement in cellular flows. Chaos, 12 (2002), pp. 481–488. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  2. D.N. Arnold, A. Mukherjee, L. Pouly. Locally adapted tetrahedral meshes using bisection. SIAM J. Sci. Comput., 22 (2000), pp. 431–448. [CrossRef] [Google Scholar]
  3. B. Audoly, H. Berestycki, Y. Pomeau. Réaction diffusion en écoulement stationnaire rapide. C. R. Acad. Sci. Paris 328, Série IIb, 2000, pp. 255–262. [Google Scholar]
  4. I. Babuška, J.E. Osborn. Eigenvalue problems. in: Handbook of Numerical Analysis. Volume II, North-Holland, 1991, pp. 641–787. [Google Scholar]
  5. I. Babuška, M. Vogelius. Feedback and adaptive finite element solution of one-dimensional boundary value problems. Numer. Math., 44 (1984), pp. 75–102. [CrossRef] [MathSciNet] [Google Scholar]
  6. C. Beattie. Galerkin eigenvector approximations. Math. Comput., 69 (2000), pp. 1400–1434. [Google Scholar]
  7. H. Berestycki, F. Hamel. Front propagation in periodic excitable media. Comm. Pure Appl. Math., 55 (2002), pp. 949–1032. [CrossRef] [MathSciNet] [Google Scholar]
  8. H. Berestycki, F. Hamel, N. Nadirashvili. Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena. Comm. Math. Physics, 253 (2005), pp 451–480. [CrossRef] [Google Scholar]
  9. L. Biferale, A. Crisanti, M. Vergassola, A. Vulpiani. Eddy diffusivities in scalar transport. Phys. Fluids, 7 (1995), pp. 2725–2734. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Bourlioux, B. Khouider. Rigorous asymptotic perspective on the large scale simulations of turbulent premixed flames. Multiscale Model. Simul., 6 (2007), pp. 287–307. [CrossRef] [Google Scholar]
  11. J. Brandts, M. Krizek. Gradient superconvergence on uniform simplicial partitions of polytopes. IMA J. Numer. Anal., 33 (2003), pp. 1–17. [Google Scholar]
  12. S. Childress, A.M. Soward. Scalar transport and alpha-effect for a family of cat’s eye flows. J. Fluid Mech, 205 (1989), pp. 99–133. [CrossRef] [Google Scholar]
  13. P. Clavin, F. Williams. Theory of premixed-flame propagation in large-scale turbulence. J. Fluid Mech., 90 (1979), pp. 598–604. [CrossRef] [Google Scholar]
  14. P. Constantin, A. Kiselev, A. Oberman, L. Ryzhik. Bulk burning rate in passive-reactive diffusion. Arch. Rat. Mech. Anal., 154 (2000), pp. 53–91. [CrossRef] [Google Scholar]
  15. R Codina. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Comput. Methods Appl. Mech. Engrg. 156 (1998), pp. 185–210. [CrossRef] [MathSciNet] [Google Scholar]
  16. X. Dai, J. Xu, A. Zhou. Convergence and optimal complexity of adaptive finite element eigenvalue computations. Numer. Math., 110 (2008), pp. 313–355. [CrossRef] [MathSciNet] [Google Scholar]
  17. T. Dombre, U. Frisch, J.M. Greene, M. Hènon, A. Mehr, A.M. Soward. Chaotic streamlines in the ABC flows, J. Fluid Mech., 67 (1986), pp. 353–391. [Google Scholar]
  18. E. Dormy, A. Soward, eds, “Mathematical Aspects of Natural Dynamics”, the Fluid Mech. of Astrophysics and Geophysics, Vol. 13, Grenoble Science and CRC Press, 2007. [Google Scholar]
  19. K. Eriksson, C. Johnson. Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems. Math. Comput., 60 (1993), pp. 167–188. [CrossRef] [Google Scholar]
  20. A. Fannjiang, G. Papanicolaou. Convection enhanced diffusion for periodic flows. SIAM J. Appl. Math., 54 (1992), pp. 333–408. [CrossRef] [MathSciNet] [Google Scholar]
  21. S. Friedlander, A. Gilbert, M. Vishik. Hydrodynamic instability for certain ABC flows. Geophys. Astrophys. Fluid Dynamics, 73 (1993), pp. 97–107. [CrossRef] [Google Scholar]
  22. S. Friedlander, M. Vishik. Dynamo theory, vorticity generation, exponential stretching. Chaos, 1(1991), pp. 198–205. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  23. T.J.R. Hughes, A.N. Brooks. A multidimensional upwind scheme with no crosswind diffusion. in: Finite Element Methods for Convection Dominated Flows (Hughes, T.J.R., ed.), New York, ASME, 1979. [Google Scholar]
  24. C. Johnson, U. Nävert, J. Pitkäranta. Finite element methods for linear hyperbolic problems. Comput. Methods Appl. Mech. Engrg., 45 (1984), pp. 285–312. [CrossRef] [MathSciNet] [Google Scholar]
  25. C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method, Combridge Univ. Press, Cambridge, 1987. [Google Scholar]
  26. A. Majda, P. Souganidis. Flame fronts in a turbulent combustion model with fractal velocity fields. Comm. Pure Appl. Math., 51 (1998), pp. 1337–1348. [CrossRef] [MathSciNet] [Google Scholar]
  27. D. Mao, L. Shen, A. Zhou. Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates. Adv. Comput. Math., 25 (2006), pp. 135–160. [CrossRef] [Google Scholar]
  28. U. Nävert. A finite element method for convection-diffsion problems, PhD thesis, Chalmers University of Technology Göteberg, 1982. [Google Scholar]
  29. J. Nolen, J. Xin. Computing reactive front speeds in random flows by variational principle. Physica D, 237 (2008), pp. 3172–3177. [CrossRef] [Google Scholar]
  30. A. Novikov, L. Ryzhik. Boundary layers and KPP fronts in a cellular flow. Arch. Ration. Mech. Anal., 184 (2007), pp. 23–48. [CrossRef] [Google Scholar]
  31. N. Peters, Turbulent Combustion, Cambridge University Press, Cambridge, 2000. [Google Scholar]
  32. M. Proctor, A. Gilbert, eds, “Lectures on Solar and Planetary Dynamos”, Publications of the Newton Institute, Cambridge Univ Press, 1994. [Google Scholar]
  33. P. Ronney. Some open issues in premixed turbulent combustion. in: Modeling in Combustion Science (J. D. Buckmaster and T. Takeno, Eds.), Lecture Notes in Physics, Vol. 449, Springer-Verlag, Berlin, pp. 3–22, 1995. [Google Scholar]
  34. H-G Roos, M. Stynes, L. Tobiska. Robust Numerical Methods for Singularly Perturbed Differential Equations, Springer series in computational mathematics, 24, second edition, 2008. [Google Scholar]
  35. L. Ryzhik, A. Zlatos. KPP pulsating front speed-up by flows. Comm. Math. Sci., 5 (2007), pp. 575–593. [Google Scholar]
  36. L. Shen, J. Xin, A. Zhou. Finite element computation of KPP front speeds in random shear flows in cylinders. Multiscale Model. Simul., 7 (2008), pp. 1029–1041. [CrossRef] [Google Scholar]
  37. L. Shen, J. Xin, A. Zhou. Finite element computation of KPP front speeds in cellular and cat’s eye flows. J. Sci. Comput., 55(2), 2013, pp. 455-470. [CrossRef] [Google Scholar]
  38. L. Shen, A. Zhou. A defect correction scheme for finite element eigenvalues with applications to quantum chemistry. SIAM J. Sci. Comput., 28 (2006), pp. 321–338 [CrossRef] [Google Scholar]
  39. G. Sivashinsky. Cascade-renormalization theory of turbulent flame speed. Combust. Sci. Tech., 62 (1988), pp. 77–96. [CrossRef] [Google Scholar]
  40. R. Verfüth. A Review of a Posteriori Error Estimates and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, New York, 1996. [Google Scholar]
  41. R. Verfüth. Robust a posteriori error estimates for stationary convection-diffusion equations. SIAM J. Numer. Anal., 43 (2005), pp. 1766–1782. [CrossRef] [MathSciNet] [Google Scholar]
  42. F. Williams, Turbulent combustion. in: The Mathematics of Combustion (J. Buckmaster, ed.), SIAM, Philadelphia, pp. 97–131, 1985. [Google Scholar]
  43. J. Xin. An Introduction to Fronts in Random Media, Surveys and Tutorials in the Applied Mathematical Sciences, Vol. 5, Springer, 2009. [Google Scholar]
  44. J. Xin, Y. Yu. Analysis and comparison of large time front speeds in turbulent combustion models., 2011. [Google Scholar]
  45. V. Yakhot. Propagation velocity of premixed turbulent flames. Comb. Sci. Tech., 60 (1988), pp. 191–214. [CrossRef] [Google Scholar]
  46. A. Zlatos. Sharp asymptotics for KPP pulsating front speed-up and diffusion enhancement by flows. Arch Rat. Mech. Anal, 195 (2010), pp.441–453. [CrossRef] [Google Scholar]
  47. A. Zlatos. Reaction-diffusion front speed enhancement by flows. Ann. Inst. H. Poincaré, Anal. Non Linaire, 28 (2011), pp. 711–726. [CrossRef] [Google Scholar]

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