A mixed finite elements approximation of inverse source problems for the wave equation with variable coefficients using observability
Numerical Analysis
2025-01-22 v1 Numerical Analysis
Optimization and Control
Abstract
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem using a space discretization based on a mixed finite element method is proposed and analyzed. Its stability and convergence relay on a new uniform boundary observability property with respect to the discretization parameter.
Cite
@article{arxiv.2501.11352,
title = {A mixed finite elements approximation of inverse source problems for the wave equation with variable coefficients using observability},
author = {Carlos Castro and Sorin Micu},
journal= {arXiv preprint arXiv:2501.11352},
year = {2025}
}