1.
Bertrand, F. & Ruas, V. A variant of the Raviart-Thomas method to handle smooth domains using straight-edged triangles. ESAIM: Mathematical Modelling and Numerical Analysis 59, 1791–1829 (2025).
2.
Bertrand, F. & Boffi, D. On the necessity of the inf-sup condition for a mixed finite element formulation. IMA Journal of Numerical Analysis 45, 1–35 (2025).
3.
Banz, L. & Bertrand, F. Contact Problems in Porous Media. Computational Methods in Applied Mathematics 25, 529–545 (2025).
4.
Bertrand, F. & Schneider, H. Least-squares finite element method for the simulation of sea-ice motion. Computers and Mathematics with Applications 172, 38–46 (2024).
5.
Bertrand, F. et al. Innovative discretizations of PDEs: Towards an accurate representation of the reality. Computers and Mathematics with Applications 176, 221–223 (2024).
6.
Bardin, R., Bertrand, F., Palii, O. & Schlottbom, M. A Phase-Space Discontinuous Galerkin Scheme for the Radiative Transfer Equation in Slab Geometry. Computational Methods in Applied Mathematics 24, 557–576 (2024).
7.
Banz, L. & Bertrand, F. A posteriori error estimate for contact problems in porous media. Computers and Mathematics with Applications 174, 219–229 (2024).
8.
Alghamdi, M., Bertrand, F., Boffi, D. & Halim, A. A Data-Driven Method for Parametric PDE Eigenvalue Problems Using Gaussian Process with Different Covariance Functions. Computational Methods in Applied Mathematics 24, 533–555 (2024).
9.
Bertrand, F. & Schneider, H. Superconvergence of DPG approximations in linear elasticity. ESAIM: Mathematical Modelling and Numerical Analysis 57, 2681–2699 (2023).
10.
Bertrand, F. & Mang, K. Recent Fails and Findings of Numerical Methods in Mechanics. Examples and Counterexamples 3, (2023).
11.
Bertrand, F., Carstensen, C., Gräßle, B. & Tran, N. T. Stabilization-free HHO a posteriori error control. Numerische Mathematik 154, 369–408 (2023).
12.
Bertrand, F., Boffi, D. & Schneider, H. Discontinuous Petrov-Galerkin Approximation of Eigenvalue Problems. Computational Methods in Applied Mathematics 23, (2023).
13.
Bertrand, F., Boffi, D. & Halim, A. Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression. Journal of Computational Physics 495, (2023).
14.
Bertrand, F., Boffi, D. & Halim, A. A reduced order model for the finite element approximation of eigenvalue problems. Computer Methods in Applied Mechanics and Engineering 404, (2023).
15.
Bertrand, F., Boffi, D. & Gastaldi, L. Approximation of the Maxwell eigenvalue problem in a least-squares setting. Computers and Mathematics with Applications 148, 302–312 (2023).
16.
Bertrand, F. Novel Raviart-Thomas Basis Functions on Anisotropic Finite Elements. Computational Methods in Applied Mathematics 23, 831–847 (2023).
17.
Bertrand, F., Moldenhauer, M. & Starke, G. Stress Equilibration for Hyperelastic Models. in Lecture Notes in Applied and Computational Mechanics vol. 98 91–105 (2022).
18.
Bertrand, F., Brodbeck, M. & Ricken, T. On robust discretization methods for poroelastic problems: Numerical examples and counter-examples. Examples and Counterexamples 2, (2022).
19.
Bertrand, F. & Brodbeck, M. Robust discretizations of poroelasticity engineering and mathematical approaches young researcher presentation in pairs. in (2022). doi:
10.23967/eccomas.2022.236.
20.
Bertrand, F. & Boffi, D. First order least-squares formulations for eigenvalue problems. IMA Journal of Numerical Analysis 42, 1339–1363 (2022).
21.
Bertrand, F. The starry night of reaction diffusion: winner or the arts & science contest. in (2022). doi:
10.23967/eccomas.2022.165.
22.
Alzaben, L., Bertrand, F. & Boffi, D. On the spectrum of the finite element approximation of a three field formulation for linear elasticity. Examples and Counterexamples 2, (2022).
23.
Alzaben, L., Bertrand, F. & Boffi, D. On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity. Computational Methods in Applied Mathematics 22, 511–528 (2022).
24.
Alghamdi, M. M.
et al. On the matching of eigensolutions to parametric partial differential equations. in (2022). doi:
10.23967/eccomas.2022.213.
25.
Bertrand, F. & Starke, G. A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem. Computers and Mathematics with Applications 91, 3–16 (2021).
26.
Bertrand, F. & Schneider, H. Least-squares methods for linear elasticity: refined error estimates. in vol. 800 1–13 (2021).
27.
Bertrand, F. & Pirch, E. Least-squares finite element method for a meso-scale model of the spread of covid-19. Computation 9, 1–22 (2021).
28.
Bertrand, F., Kober, B., Moldenhauer, M. & Starke, G. Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity. Numerical Methods for Partial Differential Equations 37, 2783–2802 (2021).
29.
Bertrand, F., Ern, A. & Radu, F. A. Robust and reliable finite element methods in poromechanics. Computers and Mathematics with Applications 91, 1–2 (2021).
30.
Bertrand, F., Demkowicz, L. & Gopalakrishnan, J. Recent Advances in Least-Squares and Discontinuous Petrov–Galerkin Finite Element Methods. Computers and Mathematics with Applications 95, 1–3 (2021).
31.
Bertrand, F., Boffi, D. & Ma, R. An Adaptive Finite Element Scheme for the Hellinger-Reissner Elasticity Mixed Eigenvalue Problem. Computational Methods in Applied Mathematics 21, 501–512 (2021).
32.
Bertrand, F., Boffi, D., Gedicke, J. & Khan, A. Some remarks on the a posteriori error analysis of the mixed laplace eigenvalue problem. in vol. 700 1–10 (2021).
33.
Bertrand, F., Boffi, D. & G. de Diego, G. Convergence analysis of the scaled boundary finite element method for the Laplace equation. Advances in Computational Mathematics 47, (2021).
34.
Bertrand, F. & Boffi, D. Least-squares formulations for eigenvalue problems associated with linear elasticity. Computers and Mathematics with Applications 95, 19–27 (2021).
35.
Bertrand, F. A Decomposition of the Raviart-Rhomas Finite Element into a Scalar and an Orientation-preserving Part. in vol. 2100 (2021).
36.
Alzaben, L., Bertrand, F. & Boffi, D. Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system. in vol. 700 1–7 (2021).
37.
Bertrand, F., Moldenhauer, M. & Starke, G. Weakly symmetric stress equilibration for hyperelastic material models. GAMM Mitteilungen 43, (2020).
38.
Bertrand, F., Kober, B., Moldenhauer, M. & Starke, G. Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity. in CISM International Centre for Mechanical Sciences, Courses and Lectures vol. 597 69–106 (2020).
39.
Bertrand, F., Boffi, D. & Stenberg, R. Asymptotically Exact A Posteriori Error Analysis for the Mixed Laplace Eigenvalue Problem. Computational Methods in Applied Mathematics 20, 215–225 (2020).
40.
Bertrand, F., Moldenhauer, M. & Starke, G. A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction. in vol. 19 663–679 (2019).
41.
Bertrand, F., Demkowicz, L., Gopalakrishnan, J. & Heuer, N. Recent Advances in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Methods. in vol. 19 395–397 (2019).
42.
Bertrand, F., Cai, Z. & Park, E. Y. Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry. in vol. 19 415–430 (2019).
43.
Bertrand, F. First-order system least-squares for interface problems. SIAM Journal on Numerical Analysis 56, 1711–1730 (2018).
44.
Bertrand, F. An alternative proof of a strip estimate for first-order system least-squares for interface problems. in vol. 10665 LNCS 95–102 (2018).
45.
Bertrand, F. & Starke, G. Parametric Raviart-Thomas elements for mixed methods on domains with curved surfaces. SIAM Journal on Numerical Analysis 54, 3648–3667 (2016).
46.
Bertrand, F., Münzenmaier, S. & Starke, G. First-order system least squares on curved boundaries: Lowest-order Raviart-Thomas elements. SIAM Journal on Numerical Analysis 52, 880–894 (2014).
47.
Bertrand, F., Münzenmaier, S. & Starke, G. First-order system least squares on curved boundaries: Higher-order Raviart-Thomas elements. SIAM Journal on Numerical Analysis 52, 3165–3180 (2014).
