Structure-preserving space discretization of differential and nonlocal constitutive relations for port-Hamiltonian systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914468204642304 |
|---|---|
| author | Bendimerad-Hohl, Antoine Haine, Ghislain Lefèvre, Laurent Matignon, Denis |
| author_facet | Bendimerad-Hohl, Antoine Haine, Ghislain Lefèvre, Laurent Matignon, Denis |
| contents | We study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, these are reduced to a finite-dimensional Lagrange subspace of a pH system thanks to a structure-preserving Finite Element Method.
To illustrate our results, the 1D nanorod case and the shear beam model are considered, which are given by differential and implicit constitutive relations for which a Stokes-Lagrange structure along with boundary energy ports naturally occur.
Then, these results are extended to the nonlinear 2D incompressible Navier-Stokes equations written in a vorticity-stream function formulation. It is first recast as a pH system defined with a Stokes-Lagrange structure along with a modulated Stokes-Dirac structure. A careful structure-preserving space discretization is then performed, leading to a finite-dimensional pH system. Theoretical and numerical results show that both enstrophy and kinetic energy evolutions are preserved both at the semi-discrete and fully-discrete levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure-preserving space discretization of differential and nonlocal constitutive relations for port-Hamiltonian systems Bendimerad-Hohl, Antoine Haine, Ghislain Lefèvre, Laurent Matignon, Denis Numerical Analysis Dynamical Systems We study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, these are reduced to a finite-dimensional Lagrange subspace of a pH system thanks to a structure-preserving Finite Element Method. To illustrate our results, the 1D nanorod case and the shear beam model are considered, which are given by differential and implicit constitutive relations for which a Stokes-Lagrange structure along with boundary energy ports naturally occur. Then, these results are extended to the nonlinear 2D incompressible Navier-Stokes equations written in a vorticity-stream function formulation. It is first recast as a pH system defined with a Stokes-Lagrange structure along with a modulated Stokes-Dirac structure. A careful structure-preserving space discretization is then performed, leading to a finite-dimensional pH system. Theoretical and numerical results show that both enstrophy and kinetic energy evolutions are preserved both at the semi-discrete and fully-discrete levels. |
| title | Structure-preserving space discretization of differential and nonlocal constitutive relations for port-Hamiltonian systems |
| topic | Numerical Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2507.06869 |