Home page of Théophile Chaumont-Frelet

theophile.chaumont (at) inria.fr Junior researcher in the Inria project-team Rapsodi Curriculum Vitae orcid

Keywords

Current postdocs and PhD students

• Sumit Mahajan (Postdoc fellow since 01/04/2025, co-supervision with Martin Vohralík)
• Florentin Proust (Ph.D. student since 01/10/2022, co-supervision with Victorita Dolean and Maxime Ingremeau)

Former postdocs and PhD students

• Zakaria Kassali (Ph.D. student from 01/11/2019 to 31/01/2023, co-supervision with Stéphane Lanteri)
• Josselin Defrance (Postdoc fellow from 01/02/2021 to 31/08/2022, co-supervision with Stéphane Lanteri)
• Patrick Vega (Postdoc fellow from 01/12/2019 to 31/05/2021, co-supervision with Stéphane Lanteri)

Publications

1. T. Chaumont-Frelet,
   An equilibrated estimator for mixed finite element discretizations of the curl-curl problem.
   IMA J. Numer. Anal. 45 no. 1, pp 329--353. 2025. preprint. doi.
2. M. Bernkopf and T. Chaumont-Frelet and J.M. Melenk,
   Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media.
   Math. Comp. 94 no. 351, pp 73--122. 2025. preprint. doi.
3. T. Chaumont-Frelet and M. Vohralík,
   A stable local commuting projector and optimal hp approximation estimates in H(curl).
   Numer. Math. 156 no. 6, pp 2293--2342. 2024. preprint. doi.
4. T. Chaumont-Frelet and V. Dolean and M. Ingremeau,
   Efficient approximation of high-frequency Helmholtz solutions by Gaussian coherent states.
   Numer. Math. 156, pp 1385--1426. 2024. preprint. doi.
5. T. Chaumont-Frelet,
   Duality analysis of interior penalty discontinuous Galerkin methods under minimal regularity and application to the a priori and a posteriori error analysis of Helmholtz problems.
   ESAIM Math. Model. Numer. Anal. 58, pp 1087--1106. 2024. preprint. doi.
6. T. Chaumont-Frelet and P. Vega,
   Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations.
   SIAM J. Numer. Anal. 62 no. 1, pp 400--421. 2024. preprint. doi.
7. T. Chaumont-Frelet,
   Asymptotically constant-free and polynomial-degree-robust a posteriori estimates for space discretizations of the wave equation.
   SIAM J. Sci. Comput. 45 no. 4, pp A1591--A1620. 2023. preprint. doi.
8. T. Chaumont-Frelet and E.A. Spence,
   Scattering by Finely Layered Obstacles: Frequency-Explicit Bounds and Homogenization.
   SIAM J. Math. Anal. 55 no. 2, pp 1319-1363. 2023. preprint. doi.
9. T. Chaumont-Frelet,
   A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem.
   Math. Comp. 92 no. 344, pp 2413--2437. 2023. preprint. doi.
10. T. Chaumont-Frelet and M. Vohralík,
    p-robust equilibrated flux reconstruction in based on local minimizations: application to a posteriori analysis of the curl-curl problem.
    SIAM J. Numer. Anal. 91 no. 4, pp 1783--1818. 2023. preprint. doi.
11. A. Modave and T. Chaumont-Frelet,
    A hybridizable discontinuous Galerkin method with characteristic variables for Helmholtz problems.
    J. Comp. Phys. 193, pp 112459. 2023. preprint. doi.
12. T. Chaumont-Frelet and S. Nicaise,
    An analysis of high-frequency Helmholtz problems in domains with conical points and their finite element discretisation.
    Comput. Meth. Appl. Math. 23 no. 4, pp 899--916. 2023. preprint. doi.
13. T. Chaumont-Frelet and A. Moiola and E.A. Spence,
    Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media.
    J. Math. Pures Appl. 179, pp 183--218. 2023. preprint. doi.
14. T. Chaumont-Frelet and A. Ern and M. Vohralík,
    Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl--curl problem..
    Math. Comp. 91, pp 37--74. 2022. preprint. doi.
15. T. Chaumont-Frelet and M.J. Grote and S. Lanteri and J.H. Tang,
    A controllability method for Maxwell's equations.
    SIAM J. Sci. Comput. 44 no. 6, pp A3700--A3727. 2022. preprint. doi.
16. T. Chaumont-Frelet and A. Ern and S. Lemaire and F. Valentin,
    Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods.
    ESAIM Math. Model. Numer. Anal. 56 no. 1, pp 261--285. 2022. preprint. doi.
17. T. Chaumont-Frelet and P. Vega,
    Frequency-explicit a posteriori error estimates for finite element discretizations of Maxwell's equations.
    SIAM J. Numer. Anal. 60 no. 4, pp 774--1798. 2022. preprint. doi.
18. T. Chaumont-Frelet and P. Vega,
    Frequency-explicit approximability estimates for time-harmonic Maxwell's equations.
    Calcolo 59 no. 2, pp 22. 2022. preprint. doi.
19. T. Chaumont-Frelet and D. Gallistl and S. Nicaise and J. Tomezyk,
    Wavenumber explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers author.
    Comun. Math. Sci. 20 no. 1, pp 1--52. 2022. preprint. doi.
20. T. Chaumont-Frelet and A. Ern and M. Vohralík,
    On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation.
    Numer. Math. 148, pp 525--573. 2021. preprint. doi.
21. T. Chaumont-Frelet and B. Verfürth,
    A generalized finite element method for problems with sign-changing coefficients.
    ESAIM Math. Model. Numer. Anal. 55 no. 3, pp 939--967. 2021. preprint. doi.
22. T. Chaumont-Frelet and M. Vohralík,
    Equivalence of local-best and global-best approximations in H(curl).
    Calcolo 58, pp 53. . preprint. doi.
23. T. Chaumont-Frelet and S. Lanteri and P. Vega,
    A posteriori error estimates for finite element discretizations of time-hamonic Maxwell's equatiosn coupled with a non-local hydrodynamic Drude model.
    Comput. Meth. Appl. Engrg. 385, pp 114002. 2021. preprint. doi.
24. T. Chaumont-Frelet and S. Nicaise,
    Wavenumber explicit convergence analysis for finite element discretizations of general wave propagation problems.
    IMA J. Numer. Anal. 40, pp 1503--1543. 2020. preprint. doi.
25. T. Chaumont-Frelet and F. Valentin,
    A multiscale hybrid-mixed method for the Helmholtz equation in heterogeneous domains.
    SIAM J. Numer. Anal. 58 no. 2, pp 1096--1067. 2020. preprint. doi.
26. T. Chaumont-Frelet and S. Nicaise and J. Tomezyk,
    Uniform a priori estimates for elliptic problems with impedance boundary conditions.
    Comm. Pure Appl. Anal. 19 no. 5, pp 2445--2471. 2020. preprint. doi.
27. V. Darrigrand and D. Pardo and T. Chaumont-Frelet and I. Gomez-Revuelto and L.E. Garcia-Castillo,
    A painless automatic hp-adatptive strategy for elliptic probems.
    Finite Elem. Anal. Des. 178, pp 103424. 2020. preprint. doi.
28. T. Chaumont-Frelet and A. Ern and M. Vohralík,
    Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron.
    C. R. Math. Acad. Sci. Paris 358 no. 9--10, pp 1101--1110. 2020. preprint. doi.
29. T. Chaumont-Frelet,
    Mixed finite element discretizations of acoustic Helmholtz problems with high wavenumbers..
    Calcolo 56, pp 49. 2019. preprint. doi.
30. T. Chaumont-Frelet and M. Shahriari and D. Pardo,
    Adjoint-based formulation for computing derivaties with respect to bed boundary positions in resistivity geophysics.
    Comput. Geosci. 23, pp 583--594. 2019. preprint. doi.
31. T. Chaumont-Frelet and S. Nicaise and D. Pardo,
    Finite element approximation of electromagnetic fields using nonfitting meshes for Geophysics.
    SIAM J. Numer. Anal. 56 no. 4, pp 2288--2321. 2018. preprint. doi.
32. T. Chaumont-Frelet and D. Pardo and Á. Rodríguez-Rozas,
    Finite element simulations of logging-while-drilling and extra-deep azimuthal resistivity measurements using non-fitting grids.
    Comput. Geosci. 22, pp 1161--1174. 2018. preprint. doi.
33. T. Chaumont-Frelet and S. Nicaise,
    High-frequency behaviour of corner singularities in Helmholtz problems.
    ESAIM Math. Model. Numer. Anal. 52 no. 5, pp 1803--2018. 2018. preprint. doi.
34. H. Barucq and T. Chaumont-Frelet and C. Gout,
    Stability analysis of heterogeneous Helmholtz problems and finite element solution based on propagation media approximation.
    Math. Comp. 86 no. 307, pp 2129--2157. 2017. preprint. doi.
35. T. Chaumont-Frelet,
    On high order methods for the heterogeneous Helmholtz equation.
    Comp. Math. Appl. 72, pp 2203--2225. 2016. preprint. doi.
36. H. Barucq and T. Chaumont-Frelet and J. Diaz and V. Péron,
    Upscaling for the Laplace problem using a discontinuous Galerkin method.
    J. Comput. Appl. Math. 240, pp 192--203. 2013. preprint. doi.

Prepublications

37. T. Chaumont-Frelet and P. Henning,
    The pollution effect for the Ginzburg-Landau equation.
    preprint.
38. T. Chaumont-Frelet,
    A ill-posed scattering problem saturating Weyl’s law.
    preprint.
39. T. Chaumont-Frelet,
    A posteriori error estimates for the finite element discretization of second-order PDEs set in unbounded domains.
    preprint.
40. A. Rappaport and T. Chaumont-Frelet and A. Modave,
    A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems.
    preprint.
41. S. Pescuma and G. Gabard and T. Chaumont-Frelet and A. Modave,
    A hybridizable Discontinuous Galerkin method with transmission variables for time-harmonic wave problems in heterogeneous media.
    preprint.
42. T. Chaumont-Frelet and G. Gantner,
    Adaptive boundary element methods for regularized combined field integral equations.
    preprint.
43. T. Chaumont-Frelet and J. Galkowski and E. Spence,
    Sharp error bounds for edge-element discretisations of the high-frequency Maxwell equations.
    preprint.
44. T. Chaumont-Frelet and J. Gedicke and L. Mascotto,
    Generalised gradients for virtual elements and applications to a posteriori error analysis.
    preprint.
45. T. Chaumont-Frelet and A. Ern,
    A priori and a posteriori analysis of the discontinuous Galerkin approximation of the time-harmonic Maxwell's equations under minimal regularity assumptions.
    preprint.
46. T. Chaumont-Frelet and A. Ern,
    Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions.
    preprint.
47. T. Chaumont-Frelet and S. Nicaise,
    Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials.
    preprint.
48. T. Chaumont-Frelet,
    Asymptotically constant-free and polynomial-degree-robust a posteriori error estimates for time-harmonic Maxwell's equations.
    preprint.
49. T. Chaumont-Frelet and E.A. Spence,
    The geometric error is less than the pollution error when solving the high-frequency Helmholtz equation with high-order FEM on curved domains.
    preprint.
50. T. Chaumont-Frelet and A. Ern,
    Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations.
    preprint.
51. T. Chaumont-Frelet and M. Ingremeau,
    Decay of coefficients and approximation rates in Gabor Gaussian frames.
    preprint.
52. T. Chaumont-Frelet and M. Vohralík,
    Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the De Rham complex.
    preprint.
53. T. Chaumont-Frelet and D. Paredes and F. Valentin,
    Flux approximation on unfitted meshes and application to multiscale hybrid-mixed methods.
    preprint.
54. G. Nehmetallah and T. Chaumont-Frelet and S. Descombes and S. Lanteri,
    A postprocessing technique for a discontinuous Galerkin discretization of time-dependent Maxwell's equations.
    preprint.