Internship and PhD Thesis
Simulation of time-dependent wave propagation problems in complex media with adaptive finite elements job info
Postdoctoral fellowship
Adaptive finite element computations for time-dependent wave propagation problems with dynamic meshes job info
Current postdocs and PhD students
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
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.
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.
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.
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.
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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.
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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.
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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.
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A. Modave and T. Chaumont-Frelet, A hybridizable discontinuous Galerkin method with characteristic variables for Helmholtz problems.
J. Comp. Phys. 193, pp 112459. 2023.
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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.
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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.
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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.
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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.
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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.
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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.
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T. Chaumont-Frelet and P. Vega, Frequency-explicit approximability estimates for time-harmonic Maxwell's equations.
Calcolo 59 no. 2, pp 22. 2022.
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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.
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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.
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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.
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T. Chaumont-Frelet and M. Vohralík, Equivalence of local-best and global-best approximations in H(curl).
Calcolo 58, pp 53. .
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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.
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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.
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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.
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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.
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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.
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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.
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T. Chaumont-Frelet, Mixed finite element discretizations of acoustic Helmholtz problems with high wavenumbers..
Calcolo 56, pp 49. 2019.
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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.
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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.
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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.
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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.
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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.
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T. Chaumont-Frelet, On high order methods for the heterogeneous Helmholtz equation.
Comp. Math. Appl. 72, pp 2203--2225. 2016.
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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
T. Chaumont-Frelet and J. Galkowski and E. Spence, Sharp error bounds for edge-element discretisations of the high-frequency Maxwell equations. preprint.
T. Chaumont-Frelet and J. Gedicke and L. Mascotto, Generalised gradients for virtual elements and applications to a posteriori error analysis. preprint.
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.
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.
T. Chaumont-Frelet and S. Nicaise, Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials. preprint.
T. Chaumont-Frelet, Asymptotically constant-free and polynomial-degree-robust a posteriori error estimates for time-harmonic Maxwell's equations. preprint.
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.
T. Chaumont-Frelet and A. Ern, Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations. preprint.
T. Chaumont-Frelet, An equilibrated estimator for mixed finite element discretizations of the curl-curl problem. preprint.
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. preprint.
T. Chaumont-Frelet and M. Ingremeau, Decay of coefficients and approximation rates in Gabor Gaussian frames. preprint.
T. Chaumont-Frelet and M. Vohralík, A stable local commuting projector and optimal hp approximation estimates in H(curl). preprint.
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.
T. Chaumont-Frelet and D. Paredes and F. Valentin, Flux approximation on unfitted meshes and application to multiscale hybrid-mixed methods. preprint.
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.