David Lafontaine

Research papers

  1. On scattering and profile decomposition for critical nonlinear waves outside weakly trapping obstacles
      With Camille Laurent
       Preprint, 2026. ArXiv
  2. Scattering for defocusing NLS with spatially dependent nonlinear damping and nonlinear trapping potential
      With Boris Shakarov
       Preprint, 2026. ArXiv
  3. Observability estimates for the Schrödinger equation on the equilateral triangle
      With Paul Alphonse
       Annales de la Faculté des Sciences de Toulouse, to appear. ArXiv
  4. Scattering for defocusing cubic NLS under locally damped strong trapping
      With Boris Shakarov
       Annales Henri Lebesgue, 2026. Journal · ArXiv
  5. Convergence of overlapping domain decomposition methods with PML transmission conditions applied to nontrapping Helmholtz problems
      With Jeffrey Galkowski, Shihua Gong, Ivan Graham, and Euan Spence
       Preprint, 2024. ArXiv
  6. The hp-FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect
      With Jeffrey Galkowski, Euan Spence and Jared Wunsch
       Communications in Mathematical Sciences, 2024. Journal · ArXiv
  7. Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
      With Euan Spence
       Pure and Applied Analysis, 2023. Journal · PDF · ArXiv
  8. Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves
      With Jeffrey Galkowski and Euan Spence
       IMA Journal of Numerical Analysis, 2023. Journal · PDF · ArXiv
  9. Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method
      With Jeffrey Galkowski, Euan Spence and Jared Wunsch
       SIAM Journal on Mathematical Analysis, 2023. Journal · PDF · ArXiv
  10. Perfectly-matched-layer truncation is exponentially accurate at high frequency
      With Jeffrey Galkowski and Euan Spence
       SIAM Journal on Mathematical Analysis, 2023. Journal · PDF · ArXiv
  11. Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation
      With Shihua Gong, Martin Gander, Ivan Graham and Euan Spence
       Numerische Mathematik, 2022. Journal · PDF · ArXiv
  12. Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients
      With Euan Spence and Jared Wunsch
       Computers & Mathematics with Applications, 2022. Journal · PDF · ArXiv
  13. A sharp relative-error bound for the Helmholtz h-FEM at high frequency
      With Euan Spence and Jared Wunsch
      Numerische Mathematik, 2021. Journal · PDF · ArXiv
  14. Scattering for critical radial Neumann waves outside a ball
      With Thomas Duyckaerts
      Revista Matemática Iberoamericana, 2021. Journal · PDF · ArXiv
  15. About the wave equation outside two strictly convex obstacles
      Communications in PDE, 2021. Journal · PDF · ArXiv
  16. For most frequencies, strong trapping has a weak effect in frequency-domain scattering
      With Euan Spence and Jared Wunsch
      Communications on Pure and Applied Mathematics, 2020. Journal · PDF · ArXiv
  17. Scattering for NLS with a sum of two repulsive potentials
      Annales de l'Institut Fourier, 2020. Journal · PDF · ArXiv
  18. Strichartz estimates without loss outside many strictly convex obstacles
       Preprint, 2018. ArXiv
  19. Strichartz estimates without loss outside two strictly convex obstacles
       Preprint, 2017. ArXiv
  20. Scattering for NLS with a potential on the line
      Asymptotic Analysis, 2016. Journal · PDF · ArXiv

Proceedings

Thesis