Publications
Banz, L., & Bertrand, F. (2025). Contact Problems in Porous Media.
Computational Methods in Applied Mathematics,
25(3), 529–545. Scopus.
https://doi.org/10.1515/cmam-2025-0012Bertrand, F., & Boffi, D. (2025). On the necessity of the inf-sup condition for a mixed finite element formulation.
IMA Journal of Numerical Analysis,
45(1), 1–35. Scopus.
https://doi.org/10.1093/imanum/drae002Bertrand, F., & Ruas, V. (2025). A variant of the Raviart- Thomas method to handle smooth domains using straight-edged triangles.
ESAIM: Mathematical Modelling and Numerical Analysis,
59(4), 1791–1829. Scopus.
https://doi.org/10.1051/m2an/2025028Bertrand, F., & Ruas, V. (2025).
A variant of the Raviart-Thomas method for smooth domains using straight-edged triangles. Scopus.
https://www.scopus.com/inward/record.uri?eid=2-s2.0-105010561286&partnerID=40&md5=6e8009f8f373372e7a128d413d30403dAlghamdi, M., Bertrand, F., Boffi, D., & Halim, A. (2024). A Data-Driven Method for Parametric PDE Eigenvalue Problems Using Gaussian Process with Different Covariance Functions.
Computational Methods in Applied Mathematics,
24(3), 533–555. Scopus.
https://doi.org/10.1515/cmam-2023-0086Banz, L., & Bertrand, F. (2024). A posteriori error estimate for contact problems in porous media[Formula presented].
Computers and Mathematics with Applications,
174, 219–229. Scopus.
https://doi.org/10.1016/j.camwa.2024.08.010Bardin, R., Bertrand, F., Palii, O., & Schlottbom, M. (2024). A Phase-Space Discontinuous Galerkin Scheme for the Radiative Transfer Equation in Slab Geometry.
Computational Methods in Applied Mathematics,
24(3), 557–576. Scopus.
https://doi.org/10.1515/cmam-2023-0090Bertrand, F., Boffi, D., Düster, A., Guermond, J.-L., Heuer, N., Li, J., & Rachowicz, W. (2024). Innovative discretizations of PDEs: Towards an accurate representation of the reality.
Computers and Mathematics with Applications,
176, 221–223. Scopus.
https://doi.org/10.1016/j.camwa.2024.10.013Bertrand, F., & Schneider, H. (2024). Least-squares finite element method for the simulation of sea-ice motion.
Computers and Mathematics with Applications,
172, 38–46. Scopus.
https://doi.org/10.1016/j.camwa.2024.07.023Bertrand, F. (2023). Novel Raviart-Thomas Basis Functions on Anisotropic Finite Elements.
Computational Methods in Applied Mathematics,
23(4), 831–847. Scopus.
https://doi.org/10.1515/cmam-2022-0235Bertrand, F., Boffi, D., & Gastaldi, L. (2023). Approximation of the Maxwell eigenvalue problem in a least-squares setting[Formula presented].
Computers and Mathematics with Applications,
148, 302–312. Scopus.
https://doi.org/10.1016/j.camwa.2023.08.010Bertrand, F., Boffi, D., & Halim, A. (2023). A reduced order model for the finite element approximation of eigenvalue problems.
Computer Methods in Applied Mechanics and Engineering,
404. Scopus.
https://doi.org/10.1016/j.cma.2022.115696Bertrand, F., Boffi, D., & Halim, A. (2023). Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression.
Journal of Computational Physics,
495. Scopus.
https://doi.org/10.1016/j.jcp.2023.112503Bertrand, F., Boffi, D., & Schneider, H. (2023). Discontinuous Petrov-Galerkin Approximation of Eigenvalue Problems.
Computational Methods in Applied Mathematics,
23(1). Scopus.
https://doi.org/10.1515/cmam-2022-0069Bertrand, F., Carstensen, C., Gräßle, B., & Tran, N. T. (2023). Stabilization-free HHO a posteriori error control.
Numerische Mathematik,
154(3–4), 369–408. Scopus.
https://doi.org/10.1007/s00211-023-01366-8Bertrand, F., & Mang, K. (2023). Editorial—Recent Fails and Findings of Numerical Methods in Mechanics.
Examples and Counterexamples,
3. Scopus.
https://doi.org/10.1016/j.exco.2022.100098Bertrand, F., & Schneider, H. (2023). Superconvergence of DPG approximations in linear elasticity.
ESAIM: Mathematical Modelling and Numerical Analysis,
57(5), 2681–2699. Scopus.
https://doi.org/10.1051/m2an/2022071Alghamdi, M. M., Bertrand, F., Boffi, D., Bonizzoni, F., Halim, A., & Priyadarshi, G. (2022).
On the matching of eigensolutions to parametric partial differential equations. World Congress in Computational Mechanics and ECCOMAS Congress. Scopus.
https://doi.org/10.23967/eccomas.2022.213Alzaben, L., Bertrand, F., & Boffi, D. (2022). On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity.
Computational Methods in Applied Mathematics,
22(3), 511–528. Scopus.
https://doi.org/10.1515/cmam-2022-0044Alzaben, L., Bertrand, F., & Boffi, D. (2022). On the spectrum of the finite element approximation of a three field formulation for linear elasticity.
Examples and Counterexamples,
2. Scopus.
https://doi.org/10.1016/j.exco.2022.100076Bertrand, F. (2022).
The starry night of reaction diffusion: Winner or the arts & science contest. World Congress in Computational Mechanics and ECCOMAS Congress. Scopus.
https://doi.org/10.23967/eccomas.2022.165Bertrand, F., & Boffi, D. (2022). First order least-squares formulations for eigenvalue problems.
IMA Journal of Numerical Analysis,
42(2), 1339–1363. Scopus.
https://doi.org/10.1093/imanum/drab005Bertrand, F., & Brodbeck, M. (2022).
Robust discretizations of poroelasticity engineering and mathematical approaches young researcher presentation in pairs. World Congress in Computational Mechanics and ECCOMAS Congress. Scopus.
https://doi.org/10.23967/eccomas.2022.236Bertrand, F., Brodbeck, M., & Ricken, T. (2022). On robust discretization methods for poroelastic problems: Numerical examples and counter-examples.
Examples and Counterexamples,
2. Scopus.
https://doi.org/10.1016/j.exco.2022.100087Bertrand, F., Moldenhauer, M., & Starke, G. (2022). Stress Equilibration for Hyperelastic Models. In
Lecture Notes in Applied and Computational Mechanics (Vol. 98, pp. 91–105). Scopus.
https://doi.org/10.1007/978-3-030-92672-4_4Alzaben, L., Bertrand, F., & Boffi, D. (2021).
Computation of eigenvalues in linear elasticity with least-squares finite elements: Dealing with the mixed system.
700, 1–7. Scopus.
https://doi.org/10.23967/wccm-eccomas.2020.095Bertrand, F. (2021).
A DECOMPOSITION OF THE RAVIART-THOMAS FINITE ELEMENT INTO A SCALAR AND AN ORIENTATION-PRESERVING PART.
2100. Scopus.
https://doi.org/10.23967/wccm-eccomas.2020.034Bertrand, F., & Boffi, D. (2021). Least-squares formulations for eigenvalue problems associated with linear elasticity.
Computers and Mathematics with Applications,
95, 19–27. Scopus.
https://doi.org/10.1016/j.camwa.2020.12.013Bertrand, F., Boffi, D., & G. de Diego, G. (2021). Convergence analysis of the scaled boundary finite element method for the Laplace equation.
Advances in Computational Mathematics,
47(3). Scopus.
https://doi.org/10.1007/s10444-021-09852-zBertrand, F., Boffi, D., Gedicke, J., & Khan, A. (2021).
Some remarks on the a posteriori error analysis of the mixed laplace eigenvalue problem.
700, 1–10. Scopus.
https://doi.org/10.23967/wccm-eccomas.2020.314Bertrand, F., Boffi, D., & Ma, R. (2021). An Adaptive Finite Element Scheme for the Hellinger-Reissner Elasticity Mixed Eigenvalue Problem.
Computational Methods in Applied Mathematics,
21(3), 501–512. Scopus.
https://doi.org/10.1515/cmam-2020-0034Bertrand, F., Demkowicz, L., & Gopalakrishnan, J. (2021). Recent Advances in Least-Squares and Discontinuous Petrov–Galerkin Finite Element Methods.
Computers and Mathematics with Applications,
95, 1–3. Scopus.
https://doi.org/10.1016/j.camwa.2021.05.029Bertrand, F., Ern, A., & Radu, F. A. (2021). Robust and reliable finite element methods in poromechanics.
Computers and Mathematics with Applications,
91, 1–2. Scopus.
https://doi.org/10.1016/j.camwa.2021.04.012Bertrand, F., Kober, B., Moldenhauer, M., & Starke, G. (2021). Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity.
Numerical Methods for Partial Differential Equations,
37(4), 2783–2802. Scopus.
https://doi.org/10.1002/num.22741Bertrand, F., & Pirch, E. (2021). Least-squares finite element method for a meso-scale model of the spread of covid-19.
Computation,
9(2), 1–22. Scopus.
https://doi.org/10.3390/computation9020018Bertrand, F., & Schneider, H. (2021).
Least-squares methods for linear elasticity: Refined error estimates.
800, 1–13. Scopus.
https://doi.org/10.23967/wccm-eccomas.2020.137Bertrand, F., & Starke, G. (2021). A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem.
Computers and Mathematics with Applications,
91, 3–16. Scopus.
https://doi.org/10.1016/j.camwa.2020.10.011Bertrand, F., Boffi, D., & Stenberg, R. (2020). Asymptotically Exact A Posteriori Error Analysis for the Mixed Laplace Eigenvalue Problem.
Computational Methods in Applied Mathematics,
20(2), 215–225. Scopus.
https://doi.org/10.1515/cmam-2019-0099Bertrand, F., Kober, B., Moldenhauer, M., & Starke, G. (2020). Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity. In
CISM International Centre for Mechanical Sciences, Courses and Lectures (Vol. 597, pp. 69–106). Scopus.
https://doi.org/10.1007/978-3-030-33520-5_3Bertrand, F., Moldenhauer, M., & Starke, G. (2020). Weakly symmetric stress equilibration for hyperelastic material models.
GAMM Mitteilungen,
43(2). Scopus.
https://doi.org/10.1002/gamm.202000007Bertrand, F., Cai, Z., & Park, E. Y. (2019).
Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry.
19(3), 415–430. Scopus.
https://doi.org/10.1515/cmam-2018-0255Bertrand, F., Demkowicz, L., Gopalakrishnan, J., & Heuer, N. (2019).
Recent Advances in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Methods.
19(3), 395–397. Scopus.
https://doi.org/10.1515/cmam-2019-0097Bertrand, F., Moldenhauer, M., & Starke, G. (2019).
A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction.
19(3), 663–679. Scopus.
https://doi.org/10.1515/cmam-2018-0004Bertrand, F. (2018).
An alternative proof of a strip estimate for first-order system least-squares for interface problems.
10665 LNCS, 95–102. Scopus.
https://doi.org/10.1007/978-3-319-73441-5_9Bertrand, F. (2018). First-order system least-squares for interface problems.
SIAM Journal on Numerical Analysis,
56(3), 1711–1730. Scopus.
https://doi.org/10.1137/16M1105827Bertrand, F., & Starke, G. (2016). Parametric Raviart-Thomas elements for mixed methods on domains with curved surfaces.
SIAM Journal on Numerical Analysis,
54(6), 3648–3667. Scopus.
https://doi.org/10.1137/15M1045442Bertrand, F., Münzenmaier, S., & Starke, G. (2014). First-order system least squares on curved boundaries: Higher-order Raviart-Thomas elements.
SIAM Journal on Numerical Analysis,
52(6), 3165–3180. Scopus.
https://doi.org/10.1137/130948902Bertrand, F., Münzenmaier, S., & Starke, G. (2014). First-order system least squares on curved boundaries: Lowest-order Raviart-Thomas elements.
SIAM Journal on Numerical Analysis,
52(2), 880–894. Scopus.
https://doi.org/10.1137/13091720X 