SPACE TIME STABILIZED FINITE ELEMENT METHODS FOR A UNIQUE CONTINUATION PROBLEM SUBJECT TO THE WAVE EQUATION - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2021

SPACE TIME STABILIZED FINITE ELEMENT METHODS FOR A UNIQUE CONTINUATION PROBLEM SUBJECT TO THE WAVE EQUATION

Abstract

We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is known in an interior subset of spacetime. For this problem, we consider a primal-dual discrete formulation of the continuum problem with the addition of stabilization terms that are designed with the goal of minimizing the numerical errors. We prove error estimates using the stability properties of the numerical scheme and a continuum observability estimate, based on the sharp geometric control condition by Bardos, Lebeau and Rauch. The order of convergence for our numerical scheme is optimal with respect to stability properties of the continuum problem and the interpolation errors of approximating with polynomial spaces. Numerical examples are provided that illustrate the methodology.
Fichier principal
Vignette du fichier
m2an190234.pdf (2.28 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02383411 , version 1 (27-11-2019)
hal-02383411 , version 2 (23-10-2020)

Identifiers

Cite

Erik Burman, Ali Feizmohammadi, Arnaud Münch, Lauri Oksanen. SPACE TIME STABILIZED FINITE ELEMENT METHODS FOR A UNIQUE CONTINUATION PROBLEM SUBJECT TO THE WAVE EQUATION. ESAIM: Mathematical Modelling and Numerical Analysis, In press, 55, pp.S969-S991. ⟨10.1051/m2an/2020062⟩. ⟨hal-02383411v2⟩
184 View
117 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More