Morgan Pierre's Publications

Accepted Papers

41. D. Dor and M. Pierre, A robust family of exponential attractors for a linear time discretization of the Cahn-Hilliard equation with a source term, ESAIM Math. Model. Numer. Anal., 58 (2024), no. 5, pp. 1755--1783.    HAL
40. M. A. Jendoubi and M. Pierre, Three remarks on the convergence of some discretized second order gradient-like systems, Nonlinear Differ. Equ. Appl., 31 (2024), no. 80.    HAL
39. D. Dor, A. Miranville and M. Pierre, Hyperbolic relaxation of the viscous Cahn-Hilliard equation with symport term for biological applications, Math. Methods Appl. Sci., 47 (2024), no. 7, pp. 5999--6035.
38. S. Zerrouq and M. Pierre, Robust optimal ship forms based on Michell's wave resistance, Math. Methods Appl. Sci., 47 (2024), no. 2, pp. 928--960.    HAL
37. M. Pierre, Maximum time step for high order BDF schemes applied to gradient flows, Calcolo, 59 (2022), no. 36.    HAL
36. M. Brachet, P. Parnaudeau and M. Pierre, Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation, Discrete Contin. Dyn. Syst. Ser. S, 15 (2022), no. 8, pp. 1987--2031.   HAL
35. J. Dambrine and M. Pierre, Continuity with respect to the speed for optimal ship forms based on Michell's formula, Math. Control Relat. Fields, 13 (2023), no. 1, pp. 63--93.    HAL
34. M. Pierre, Maximum time step for the BDF3 scheme applied to gradient flows, Calcolo, 58 (2021), no. 3.    HAL
33. J. Fourdrinoy, J. Dambrine, M. Petcu, M. Pierre and G. Rousseaux, The dual nature of the dead-water phenomenology: Nansen versus Ekman wave-making drags, Proc. Natl. Acad. Sci. USA, 117 (July 21, 2020), no. 29, pp. 16770--16775.
32. J. Dambrine, E. Noviani and M. Pierre, Rankine-type cylinders having zero wave resistance in infinitely deep flows, IMA J. Appl. Math., 85 (2020), no. 3, pp. 343--364.    HAL
31. A. Bouchriti, M. Pierre and N. E. Alaa, Remarks on the asymptotic behavior of scalar auxiliary variable (SAV) schemes for gradient-like flows, J. Appl. Anal. Comput., 10 (2020), no. 5, pp. 2198--2219    HAL
30. F. D. R. Langa and M. Pierre, A doubly splitting scheme for the Caginalp system with singular potentials and dynamic boundary conditions, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), no. 2, pp. 653--676.    HAL
29. A. Bouchriti, M. Pierre and N. E. Alaa, Gradient stability of high-order BDF methods and some applications, J. Difference Equ. Appl., 26 (2020), no. 1, pp. 74--103.    HAL
28. A. Bouchriti, M. Pierre and N. E. Alaa, Simulation of the transmission line equation by a high-order FDTD method, An. Univ. Craiova Ser. Mat. Inform. 46 (2019), no. 2, pp. 410--425.
27. H. Khalfi, M. Pierre, N. E. Alaa and M. Guedda Convergence to equilibrium of a DC algorithm for an epitaxial growth model, Int. J. Numer. Anal. Model. 16 (2019), no. 3, pp. 398--411.
26. M. Pierre, Convergence of exponential attractors for a finite element approximation of the Allen-Cahn equation, Numer. Funct. Anal. Optim., 39 (2018), no. 16, pp.1755--1784.    HAL
25. J. Dambrine and M. Pierre, Regularity of optimal ship forms based on Michell's wave resistance, Appl. Math. Optim. 82 (2020), pp. 23--62.    HAL
24. M. Pierre, Convergence of exponential attractors for a time semi-discrete reaction-diffusion equation, Numer. Math. 139 (2018), no. 1, pp. 121--153.    HAL
23. N. Batangouna and M. Pierre Convergence of exponential attractors for a time splitting approximation of the Caginalp phase-field system, Commun. Pure Appl. Anal. 17 (2018), no. 1, pp. 1--19.
22. P. F. Antonietti, B. Merlet, M. Pierre and M. Verani Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation, AIMS Mathematics 1 (2016), no. 3, pp. 178--194.
21. M. Pierre and Ph. Rogeon, Convergence to equilibrium for a time semi-discrete damped wave equation, J. Appl. Anal. Comput. 6 (2016), no. 4, pp.1041-1048.
20. M. Grasselli and M. Pierre, Energy stable and convergent finite element schemes for the modified phase field crystal equation, ESAIM Math. Model. Numer. Anal. 50 (2016), no. 5, pp. 1523--1560. HAL
19. J. Dambrine, M. Pierre and G. Rousseaux, A theoretical and numerical determination of optimal ship forms based on Michell's wave resistance, ESAIM Control Optim. Calc. Var. 22 (2016), no. 1, pp. 88--111. ArXiv
18. Mi. Pierre and Mo. Pierre, Global Existence via a Mutivalued Operator for an Allen-Cahn-Gurtin Equation, Discrete Contin. Dyn. Syst., 33 (2013), no. 11 & 12, pp. 5347--5377.
17. N. E. Alaa and M. Pierre, Convergence to equilibrium for discretized gradient-like systems with analytic features, IMA J. Numer. Anal. 33 (2013), pp. 1291--1321.
16. M. Grasselli and M. Pierre, Convergence to equilibrium of solutions of the backward Euler scheme for asymptotically autonomous second-order gradient-like systems, Commun. Pure Appl. Anal., 11 (2012), no.6, pp. 2393--2416.
15. M. Pierre and A. Rougirel, Stationary solutions to phase field crystal equations, Math. Methods Appl. Sci., 34 (2011), no. 3, pp. 278--308.    HAL
14. S. Injrou and M. Pierre, Error estimates for a finite element discretization of the Cahn-Hilliard-Gurtin equations , Adv. Differential Equations, 15 (2010), no. 11-12, pp. 1161--1192.
13. L. Cherfils, M. Petcu and M. Pierre, A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions, Discrete Contin. Dyn. Syst., 27 (2010), no. 4, pp. 1511--1533.
12. M. Grasselli and M. Pierre, A splitting method for the Cahn-Hilliard equation with inertial term, Math. Models Methods Appl. Sci. 20 (2010), no. 8, pp. 1363--1390.
11. B. Merlet and M. Pierre, Convergence to equilibrium for the backward Euler scheme and applications, Commun. Pure Appl. Anal. 9 (2010), no. 3, pp. 685--702.
10. M. Pierre, Uniform convergence for a finite element discretization of a viscous diffusion equation, IMA J. Numer. Anal. 30 (2010), no. 2, pp. 487--511.
9. L. Cherfils and M. Pierre, Non-global existence for an Allen-Cahn-Gurtin equation with logarithmic free energy, J. Evol. Equ. 8 (2008), no. 4, pp. 727--748.
8. S. Injrou and M. Pierre, Stable discretizations of the Cahn-Hilliard-Gurtin equations, Discrete Contin. Dyn. Syst., 22 (2008), no. 4, pp. 1065--1080.
7. M. Pierre, Symmetric boundary values for the Dirichlet problem for harmonic maps from the disc into the 2-sphere, Calc. Var. Partial Differential Equations, 31 (2008), no. 2, pp. 147--166.
6. O. Binda and M. Pierre, Asymptotic expansion for a delay differential equation with continuous and piecewise constant arguments, Funkcial. Ekvac., 50 (2007), no. 3, pp. 421--448.
5. M. Pierre, Symmetry breaking for the Dirichlet problem for harmonic maps from the disc into the 2-sphere, Adv. Differential Equations, 10 (2005), no. 6, pp. 675--694.
4. B. Merlet and M. Pierre, Moving mesh for the axisymmetric harmonic map flow, M2AN Math. Model. Numer. Anal., 39 (2005), no. 4, pp.781--796.
3. M. Pierre, Weak BV convergence of a moving finite element method for singular axisymmetric harmonic maps, SIAM J. Numer. Anal., 43 (2005), no. 4, pp. 1436--1454.
2. F. Alouges and M. Pierre, Mesh optimization for singular axisymmetric harmonic maps from the disc into the sphere, Numer. Math., 101 (2005), no. 3, pp. 391--414.
1. M. Pierre, Newton and conjugate gradient for harmonic maps from the disc into the sphere, ESAIM Control Optim. Calc. Var. 10 (2004), no. 1, pp. 142--167.

Proceedings

4. J. Fourdrinoy, C. Caplier, Y. Devaux, G. Rousseaux, A. Gianni et al., The naval battle of Actium and the myth of the ship-holder: the effect of bathymetry, 5th MASHCON - International Conference on Ship Manoeuvring in Shallow and Confined Water with non-exclusive focus on manoeuvring in waves, wind and current, Flanders Hydraulics Research; Maritime Technology Division, Ghent University, May 2019, Ostend, Belgium. WWC007 (pp 104 - 133) HAL
3. J. Dambrine, M. Pierre and G. Rousseaux, Optimization of ship hulls considered as slender bodies, joint SHF/AIPCN Conference, Meudon, France, 18-19 November 2015.
2. N. James, D. Biau, J. Dambrine, M. Pierre and E. Lamballais, Assessment of immersed boundary methods toward high accuracy, joint EUROMECH/ERCOFTAC Colloquium 549, Leiden, The Netherlands, 17-19 June 2013.
1. M. Grasselli, N. Lecoq and M. Pierre, A long-time stable fully discrete approximation of the Cahn-Hilliard equation with inertial term, DCDS Supplements, 2011 (2011), Issue Special, pp. 543--552.

Convergence to equilibrium for the Cahn-Hilliard equation on the unit cube (see Ref. 36) ut=-∆2u+ ε-2 ∆ (u3-u) ε=0.04 / time step dt=1e-7 random initial value Finite difference discretization in space linear IMEX (implicit-explicit) discretization in time The 2D and 3D PYTHON code is available here.

An optimal ship hull based on Michell's wave resistance formula (see Refs. 25 and 35)

The BDF6 method is not quadratically stable (see Ref. 37)

Convergence to equilibrium for the Cahn-Hilliard equation on the unit disc (see Ref. 11) ut=-α∆2u+ ∆ (u3-u) α=0.05 / time step dt=0.015 / 600 iterations random initial value P1-P1 Finite element discretization in space backward Euler discretization in time Software: FreeFem++

Convergence to equilibrium for the Modified Phase Field Crystal equation (see Ref. 20) βutt+ut=Δ[∆2u+ 2∆u+u3+(1-ε)u] on the square (0,6π)x(0,6π) with periodic boundary conditions β=0.1 / ε=2 / time step dt=0.25 / 200 iterations initial value u0(x,y)=0.2+0.2cos(x)cos(y) and ut(0)=0 P1-P1-P1 Finite element discretization in space 2nd order discretization in time (scheme of Gomez and Hughes) Software: FreeFem++