Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Toledo-Zucco, Jesus-Pablo, Matignon, Denis, Poussot-Vassal, Charles
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914664311422976
author Toledo-Zucco, Jesus-Pablo
Matignon, Denis
Poussot-Vassal, Charles
author_facet Toledo-Zucco, Jesus-Pablo
Matignon, Denis
Poussot-Vassal, Charles
contents A structure-preserving Finite Element Method (FEM) for the transport equation in one- and two-dimensional domains is presented. This Distributed Parameter System (DPS) has non-collocated boundary control and observation, and reveals a scattering-energy preserving structure. We show that the discretized model preserves the aforementioned structure from the original infinite-dimensional system. Moreover, we analyse the case of moving meshes for the one-dimensional case. The moving mesh requires less states than the fixed one to produce solutions with a comparable accuracy, and it can also reduce the overshoot and oscillations of Gibbs phenomenon produced when using the FEM. Numerical simulations are provided for the case of a one-dimensional transport equation with fixed and moving meshes.
format Preprint
id arxiv_https___arxiv_org_abs_2402_01232
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh
Toledo-Zucco, Jesus-Pablo
Matignon, Denis
Poussot-Vassal, Charles
Numerical Analysis
Systems and Control
A structure-preserving Finite Element Method (FEM) for the transport equation in one- and two-dimensional domains is presented. This Distributed Parameter System (DPS) has non-collocated boundary control and observation, and reveals a scattering-energy preserving structure. We show that the discretized model preserves the aforementioned structure from the original infinite-dimensional system. Moreover, we analyse the case of moving meshes for the one-dimensional case. The moving mesh requires less states than the fixed one to produce solutions with a comparable accuracy, and it can also reduce the overshoot and oscillations of Gibbs phenomenon produced when using the FEM. Numerical simulations are provided for the case of a one-dimensional transport equation with fixed and moving meshes.
title Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh
topic Numerical Analysis
Systems and Control
url https://arxiv.org/abs/2402.01232