Uniform boundary stabilization of a high-order finite element space discretization of the 1-d wave equation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2024

Uniform boundary stabilization of a high-order finite element space discretization of the 1-d wave equation

Abstract

The objective of this work is to propose and analyze numerical schemes for solving boundary control problems or data assimilation problems by observers for wave propagation problems. The efficiency of the considered control or data assimilation strategy relies on the exponentially stable character of the underlying system. Therefore, the aim of our work is to propose a discretization process that allows preserving the exponential stability at the discrete level when using high-order spectral finite element approximation. The main idea is to add a stabilizing term to the wave equation that dampens the spurious oscillatory components of the solutions. This term is based on a discrete multiplier analysis that gives us the exponential stability of the semi-discrete problem at any order without affecting the approximation properties.
Fichier principal
Vignette du fichier
UniformStabWave.pdf (1.29 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04172229 , version 1 (27-07-2023)
hal-04172229 , version 2 (03-05-2024)

Licence

Identifiers

  • HAL Id : hal-04172229 , version 2

Cite

Tiphaine Delaunay, Sébastien Imperiale, Philippe Moireau. Uniform boundary stabilization of a high-order finite element space discretization of the 1-d wave equation. 2024. ⟨hal-04172229v2⟩
113 View
58 Download

Share

Gmail Mastodon Facebook X LinkedIn More