Open Access
Issue
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
Page(s) 331 - 362
DOI https://doi.org/10.1051/m2an/2024075
Published online 14 January 2025
  1. U. Ayachit, The ParaView Guide: A Parallel Visualization Application. Kitware, Inc. (2015). [Google Scholar]
  2. F.B. Belgacem, The Mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–197. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Berestycki and L. Rossi, Reaction-diffusion equations for population dynamics with forced speed I – The case of the whole space. Discrete Continuous Dyn. Syst. 21 (2008) 41. [CrossRef] [MathSciNet] [Google Scholar]
  4. H. Berestycki and L. Rossi, Reaction-diffusion equations for population dynamics with forced speed II – Cylindrical-type domains. Discrete Continuous Dyn. Syst. 25 (2009) 19. [CrossRef] [MathSciNet] [Google Scholar]
  5. H. Berestycki, O. Diekmann, C. Nagelkerke and P. Zegeling, Can a species keep pace with a shifting climate? Bull. Math. Biol. 71 (2009) 339–429. [Google Scholar]
  6. C. Bernardi, C. Canuto and Y. Maday, Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem. SIAM J. Numer. Anal. 25 (1988) 1237–1271. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Bernardi, Y. Maday and A.T. Patera, Domain decomposition by the mortar element method, in Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters. Springer (1993) 269–286. [Google Scholar]
  8. C. Bernardi, Y. Maday and A.T. Patera, A new conforming approach to domain decomposition: the mortar element method, in Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, edited by H. Brézis and J.L. Lions. Vol. XI. (1994). [Google Scholar]
  9. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Vol. 44. Springer (2013). [Google Scholar]
  10. J. Bouhours and T. Giletti, Spreading and Vanishing for a Monostable Reaction–Diffusion Equation with Forced Speed. J. Dyn. Differ. Equ. 31 (2019) 247–286. [CrossRef] [Google Scholar]
  11. E. Burman, S. Claus, P. Hansbo, M.G. Larson and A. Massing, CutFEM: discretizing geometry and partial differential equations. Int. J. Numer. Methods Eng. 104 (2015) 472–501. [CrossRef] [Google Scholar]
  12. R.S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations. John Wiley & Sons (2004). [CrossRef] [Google Scholar]
  13. I.-C. Chen, J.K. Hill, R. Ohlemüller, D.B. Roy and C.D. Thomas, Rapid range shifts of species associated with high levels of climate warming. Science 333 (2011) 1024–1026. [CrossRef] [PubMed] [Google Scholar]
  14. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. SIAM (2002). [Google Scholar]
  15. C.A. Cobbold and R. Stana, Should I stay or should I go: partially sedentary populations can outperform fully dispersing populations in response to climate-induced range shifts. Bull. Math. Biol. 82 (2020) 1–21. [CrossRef] [Google Scholar]
  16. J. Donea, A. Huerta, J.-P. Ponthot and A. Rodríguez-Ferran, Chapter 14: arbitrary Lagrangian–Eulerian methods, in Examine Basic Concepts Behind Interpolation, Error Estimation, Computer Algebra and Geometric Modelling in Computational Mechanics. Business Wire (2006). [Google Scholar]
  17. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Vol. 159. Springer (2004). [CrossRef] [Google Scholar]
  18. L.C. Evans, Partial Differential Equations, 2nd edition. Vol. 19. American Mathematical Society (2010). [Google Scholar]
  19. R.I. Fernandes, B. Bialecki and G. Fairweather, An ADI extrapolated Crank–Nicolson orthogonal spline collocation method for nonlinear reaction–diffusion systems on evolving domains. J. Comput. Phys. 299 (2015) 561–580. [CrossRef] [MathSciNet] [Google Scholar]
  20. B.E. Griffith and N.A. Patankar, Immersed methods for fluid–structure interaction. Ann. Rev. Fluid Mech. 52 (2020) 421–448. [CrossRef] [PubMed] [Google Scholar]
  21. P. Grisvard, Elliptic Problems in Nonsmooth Domains. SIAM (2011). [CrossRef] [Google Scholar]
  22. F. Hecht, New developments in FreeFem++. J. Numer. Math. 20 (2012) 251–265. [CrossRef] [MathSciNet] [Google Scholar]
  23. B. John, P. Senthilkumar and S. Sadasivan, Applied and theoretical aspects of conjugate heat transfer analysis: a review. Arch. Comput. Methods Eng. 26 (2019) 475–489. [CrossRef] [MathSciNet] [Google Scholar]
  24. Z. Li, An overview of the immersed interface method and its applications. Taiwanese J. Math. 7 (2003) 1–49. [MathSciNet] [Google Scholar]
  25. P. Lidström, Moving regions in Euclidean space and Reynolds’ transport theorem. Math. Mech. Solids 16 (2011) 366–380. [CrossRef] [MathSciNet] [Google Scholar]
  26. D. Ludwig, D. Aronson and H. Weinberger, Spatial patterning of the spruce budworm. J. Math. Biol. 8 (1979) 217–258. [CrossRef] [MathSciNet] [Google Scholar]
  27. F. Lutscher and G. Seo, The effect of temporal variability on persistence conditions in rivers. J. Theor. Biol. 283 (2011) 53–59. [CrossRef] [Google Scholar]
  28. F. Lutscher, M.A. Lewis and E. McCauley, Effects of heterogeneity on spread and persistence in rivers. Bull. Math. Biol. 68 (2006) 2129–2160. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  29. J.S. MacDonald and F. Lutscher, Individual behavior at habitat edges may help populations persist in moving habitats. J. Math. Biol. 77 (2018) 2049–2077. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  30. J.S. MacDonald, Y. Bourgault and F. Lutscher, Moving-habitat models: a numerical approach. Math. Biosci. 341 (2021) 108711. [CrossRef] [Google Scholar]
  31. G.A. Maciel and F. Lutscher, How individual movement response to habitat edges affects population persistence and spatial spread. Am. Nat. 182 (2013) 42–52. [CrossRef] [PubMed] [Google Scholar]
  32. C. Mavriplis, Nonconforming discretizations and a posteriori error estimators for adaptive spectral element techniques. Ph.D. Thesis, Massachusetts Institute of Technology (1989). [Google Scholar]
  33. R.A. Nicolaides, Existence, uniqueness and approximation for generalized saddle point problems. SIAM J. Numer. Anal. 19 (1982) 349–357. [CrossRef] [MathSciNet] [Google Scholar]
  34. O. Ovaskainen and S.J. Cornell, Biased movement at a boundary and conditional occupancy times for diffusion processes. J. Appl. Prob. 40 (2003) 557–580. [CrossRef] [Google Scholar]
  35. A. Phillips and M. Kot, Persistence in a two-dimensional moving-habitat model. Bull. Math. Biol. 77 (2015) 2125–2159. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  36. A.B. Potapov and M.A. Lewis, Climate and competition: the effect of moving range boundaries on habitat invasibility. Bull. Math. Biol. 66 (2004) 975–1008. [CrossRef] [MathSciNet] [Google Scholar]
  37. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations. Number BOOK. Oxford University Press (1999). [Google Scholar]
  38. P.-A. Raviart and J.-M. Thomas, Primal hybrid finite element methods for 2nd order elliptic equations. Math. Comput. 31 (1977) 391–413. [CrossRef] [Google Scholar]
  39. R. Sacco, A.G. Mauri and G. Guidoboni, A stabilized dual mixed hybrid finite element method with Lagrange multipliers for three-dimensional elliptic problems with internal interfaces. J. Sci. Comput. 82 (2020) 1–31. [CrossRef] [MathSciNet] [Google Scholar]
  40. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [Google Scholar]
  41. W. Shen, Z. Shen, S. Xue and D. Zhou, Population dynamics under climate change: persistence criterion and effects of fluctuations. J. Math. Biol. 84 (2022) 1–42. [CrossRef] [MathSciNet] [Google Scholar]
  42. H.-H. Vo, Persistence versus extinction under a climate change in mixed environments. J. Differ. Equ. 259 (2015) 4947–4988. [CrossRef] [Google Scholar]
  43. Y. Wang, J. Shi and J. Wang, Persistence and extinction of population in reaction–diffusion–advection model with strong allee effect growth. J. Math. Biol. 78 (2019) 2093–2140. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  44. Y. Zhou and W.F. Fagan, A discrete-time model for population persistence in habitats with time-varying sizes. J. Math. Biol. 75 (2017) 649–704. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you