49.
Bertrand, F., Brodbeck, M., Ricken, T. & Schneider, H. Least-Squares finite element methods for nonlinear problems: A unified framework. Computers & Mathematics with Applications 218, 435–451 (2026) doi:10.1016/j.camwa.2026.06.035.
48.
Bertrand, F. & Dağlı, T. A Numerical Study of a Weakly Symmetric Dual-Mixed Finite Element Method for the Stokes Source Problem With Velocity Postprocessing. Proceedings in Applied Mathematics and Mechanics (2026) doi:10.1002/pamm.70232.
47.
Banz, L. & Bertrand, F. Contact Problems in Porous Media. Computational Methods in Applied Mathematics 25, 529–545 (2025) doi:10.1515/cmam-2025-0012.
46.
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) doi:10.1093/imanum/drae002.
45.
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) doi:10.1051/m2an/2025028.
44.
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) doi:10.1515/cmam-2023-0086.
43.
Banz, L. & Bertrand, F. A posteriori error estimate for contact problems in porous media. Computers and Mathematics with Applications 174, 219–229 (2024) doi:10.1016/j.camwa.2024.08.010.
42.
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) doi:10.1515/cmam-2023-0090.
41.
Bertrand, F. et al. Innovative discretizations of PDEs: Towards an accurate representation of the reality. Computers and Mathematics with Applications 176, 221–223 (2024) doi:10.1016/j.camwa.2024.10.013.
40.
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) doi:10.1016/j.camwa.2024.07.023.
39.
Bertrand, F. Novel Raviart-Thomas Basis Functions on Anisotropic Finite Elements. Computational Methods in Applied Mathematics 23, 831–847 (2023) doi:10.1515/cmam-2022-0235.
38.
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) doi:10.1016/j.camwa.2023.08.010.
37.
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) doi:10.1016/j.cma.2022.115696.
36.
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) doi:10.1016/j.jcp.2023.112503.
35.
Bertrand, F., Boffi, D. & Schneider, H. Discontinuous Petrov-Galerkin Approximation of Eigenvalue Problems. Computational Methods in Applied Mathematics 23, (2023) doi:10.1515/cmam-2022-0069.
34.
Bertrand, F., Carstensen, C., Gräßle, B. & Tran, N. T. Stabilization-free HHO a posteriori error control. Numerische Mathematik 154, 369–408 (2023) doi:10.1007/s00211-023-01366-8.
33.
Bertrand, F. & Mang, K. Recent Fails and Findings of Numerical Methods in Mechanics. Examples and Counterexamples 3, (2023) doi:10.1016/j.exco.2022.100098.
32.
Bertrand, F. & Schneider, H. Superconvergence of DPG approximations in linear elasticity. ESAIM: Mathematical Modelling and Numerical Analysis 57, 2681–2699 (2023) doi:10.1051/m2an/2022071.
31.
Alghamdi, M. M. et al. On the matching of eigensolutions to parametric partial differential equations. in (2022) doi:10.23967/eccomas.2022.213.
30.
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) doi:10.1515/cmam-2022-0044.
29.
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) doi:10.1016/j.exco.2022.100076.
28.
Bertrand, F. The starry night of reaction diffusion: winner or the arts & science contest. in (2022) doi:10.23967/eccomas.2022.165.
27.
Bertrand, F. & Boffi, D. First order least-squares formulations for eigenvalue problems. IMA Journal of Numerical Analysis 42, 1339–1363 (2022) doi:10.1093/imanum/drab005.
26.
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.
25.
Bertrand, F., Brodbeck, M. & Ricken, T. On robust discretization methods for poroelastic problems: Numerical examples and counter-examples. Examples and Counterexamples 2, (2022) doi:10.1016/j.exco.2022.100087.
24.
Bertrand, F., Moldenhauer, M. & Starke, G. Stress Equilibration for Hyperelastic Models. in Lecture Notes in Applied and Computational Mechanics vol. 98 91–105 (2022) doi:10.1007/978-3-030-92672-4_4.
23.
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) doi:10.23967/wccm-eccomas.2020.095.
22.
Bertrand, F. A Decomposition of the Raviart-Rhomas Finite Element into a Scalar and an Orientation-preserving Part. in vol. 2100 (2021) doi:10.23967/wccm-eccomas.2020.034.
21.
Bertrand, F. & Boffi, D. Least-squares formulations for eigenvalue problems associated with linear elasticity. Computers and Mathematics with Applications 95, 19–27 (2021) doi:10.1016/j.camwa.2020.12.013.
20.
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) doi:10.1007/s10444-021-09852-z.
19.
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) doi:10.23967/wccm-eccomas.2020.314.
18.
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) doi:10.1515/cmam-2020-0034.
17.
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) doi:10.1016/j.camwa.2021.05.029.
16.
Bertrand, F., Ern, A. & Radu, F. A. Robust and reliable finite element methods in poromechanics. Computers and Mathematics with Applications 91, 1–2 (2021) doi:10.1016/j.camwa.2021.04.012.
15.
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) doi:10.1002/num.22741.
14.
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) doi:10.3390/computation9020018.
13.
Bertrand, F. & Schneider, H. Least-squares methods for linear elasticity: refined error estimates. in vol. 800 1–13 (2021) doi:10.23967/wccm-eccomas.2020.137.
12.
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) doi:10.1016/j.camwa.2020.10.011.
11.
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) doi:10.1515/cmam-2019-0099.
10.
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) doi:10.1007/978-3-030-33520-5_3.
9.
Bertrand, F., Moldenhauer, M. & Starke, G. Weakly symmetric stress equilibration for hyperelastic material models. GAMM Mitteilungen 43, (2020) doi:10.1002/gamm.202000007.
8.
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) doi:10.1515/cmam-2018-0255.
7.
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) doi:10.1515/cmam-2019-0097.
6.
Bertrand, F., Moldenhauer, M. & Starke, G. A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction. in vol. 19 663–679 (2019) doi:10.1515/cmam-2018-0004.
5.
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) doi:10.1007/978-3-319-73441-5_9.
4.
Bertrand, F. First-order system least-squares for interface problems. SIAM Journal on Numerical Analysis 56, 1711–1730 (2018) doi:10.1137/16M1105827.
3.
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) doi:10.1137/15M1045442.
2.
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) doi:10.1137/130948902.
1.
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) doi:10.1137/13091720X.
35.
Bertrand, F., Brodbeck, M., Ricken, T. & Schneider, H. Least-Squares finite element methods for nonlinear problems: A unified framework. Computers & Mathematics with Applications 218, 435–451 (2026) doi:10.1016/j.camwa.2026.06.035.
34.
Banz, L. & Bertrand, F. Contact Problems in Porous Media. Computational Methods in Applied Mathematics 25, 529–545 (2025) doi:10.1515/cmam-2025-0012.
33.
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) doi:10.1093/imanum/drae002.
32.
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) doi:10.1051/m2an/2025028.
31.
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) doi:10.1515/cmam-2023-0086.
30.
Banz, L. & Bertrand, F. A posteriori error estimate for contact problems in porous media. Computers and Mathematics with Applications 174, 219–229 (2024) doi:10.1016/j.camwa.2024.08.010.
29.
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) doi:10.1515/cmam-2023-0090.
28.
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) doi:10.1016/j.camwa.2024.07.023.
27.
Bertrand, F. Novel Raviart-Thomas Basis Functions on Anisotropic Finite Elements. Computational Methods in Applied Mathematics 23, 831–847 (2023) doi:10.1515/cmam-2022-0235.
26.
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) doi:10.1016/j.camwa.2023.08.010.
25.
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) doi:10.1016/j.cma.2022.115696.
24.
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) doi:10.1016/j.jcp.2023.112503.
23.
Bertrand, F., Carstensen, C., Gräßle, B. & Tran, N. T. Stabilization-free HHO a posteriori error control. Numerische Mathematik 154, 369–408 (2023) doi:10.1007/s00211-023-01366-8.
22.
Bertrand, F. & Schneider, H. Superconvergence of DPG approximations in linear elasticity. ESAIM: Mathematical Modelling and Numerical Analysis 57, 2681–2699 (2023) doi:10.1051/m2an/2022071.
21.
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) doi:10.1515/cmam-2022-0044.
20.
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) doi:10.1016/j.exco.2022.100076.
19.
Bertrand, F. & Boffi, D. First order least-squares formulations for eigenvalue problems. IMA Journal of Numerical Analysis 42, 1339–1363 (2022) doi:10.1093/imanum/drab005.
18.
Bertrand, F., Brodbeck, M. & Ricken, T. On robust discretization methods for poroelastic problems: Numerical examples and counter-examples. Examples and Counterexamples 2, (2022) doi:10.1016/j.exco.2022.100087.
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) doi:10.1007/978-3-030-92672-4_4.
16.
Bertrand, F. & Boffi, D. Least-squares formulations for eigenvalue problems associated with linear elasticity. Computers and Mathematics with Applications 95, 19–27 (2021) doi:10.1016/j.camwa.2020.12.013.
15.
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) doi:10.1007/s10444-021-09852-z.
14.
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) doi:10.1515/cmam-2020-0034.
13.
Bertrand, F., Ern, A. & Radu, F. A. Robust and reliable finite element methods in poromechanics. Computers and Mathematics with Applications 91, 1–2 (2021) doi:10.1016/j.camwa.2021.04.012.
12.
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) doi:10.1002/num.22741.
11.
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) doi:10.3390/computation9020018.
10.
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) doi:10.1016/j.camwa.2020.10.011.
9.
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) doi:10.1515/cmam-2019-0099.
8.
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) doi:10.1007/978-3-030-33520-5_3.
7.
Bertrand, F., Moldenhauer, M. & Starke, G. Weakly symmetric stress equilibration for hyperelastic material models. GAMM Mitteilungen 43, (2020) doi:10.1002/gamm.202000007.
6.
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) doi:10.1515/cmam-2018-0255.
5.
Bertrand, F., Moldenhauer, M. & Starke, G. A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction. in vol. 19 663–679 (2019) doi:10.1515/cmam-2018-0004.
4.
Bertrand, F. First-order system least-squares for interface problems. SIAM Journal on Numerical Analysis 56, 1711–1730 (2018) doi:10.1137/16M1105827.
3.
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) doi:10.1137/15M1045442.
2.
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) doi:10.1137/130948902.
1.
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) doi:10.1137/13091720X.
9.
Bertrand, F. & Dağlı, T. A Numerical Study of a Weakly Symmetric Dual-Mixed Finite Element Method for the Stokes Source Problem With Velocity Postprocessing. Proceedings in Applied Mathematics and Mechanics (2026) doi:10.1002/pamm.70232.
8.
Alghamdi, M. M. et al. On the matching of eigensolutions to parametric partial differential equations. in (2022) doi:10.23967/eccomas.2022.213.
7.
Bertrand, F. The starry night of reaction diffusion: winner or the arts & science contest. in (2022) doi:10.23967/eccomas.2022.165.
6.
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.
5.
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) doi:10.23967/wccm-eccomas.2020.095.
4.
Bertrand, F. A Decomposition of the Raviart-Rhomas Finite Element into a Scalar and an Orientation-preserving Part. in vol. 2100 (2021) doi:10.23967/wccm-eccomas.2020.034.
3.
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) doi:10.23967/wccm-eccomas.2020.314.
2.
Bertrand, F. & Schneider, H. Least-squares methods for linear elasticity: refined error estimates. in vol. 800 1–13 (2021) doi:10.23967/wccm-eccomas.2020.137.
1.
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) doi:10.1007/978-3-319-73441-5_9.
Editorial appointments
- Managing Editor — Computers & Mathematics with Applications (CAMWA)
- Managing Editor — GAMMath
- Editor-in-Chief — Examples and Counterexamples (EXCO)
Editorial publications (5)
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) doi:10.1016/j.camwa.2024.10.013.
4.
Bertrand, F., Boffi, D. & Schneider, H. Discontinuous Petrov-Galerkin Approximation of Eigenvalue Problems. Computational Methods in Applied Mathematics 23, (2023) doi:10.1515/cmam-2022-0069.
3.
Bertrand, F. & Mang, K. Recent Fails and Findings of Numerical Methods in Mechanics. Examples and Counterexamples 3, (2023) doi:10.1016/j.exco.2022.100098.
2.
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) doi:10.1016/j.camwa.2021.05.029.
1.
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) doi:10.1515/cmam-2019-0097.