Well-posedness of first-order acoustic wave equations and space-time finite element approximation
Numerical Analysis
2023-11-20 v1 Numerical Analysis
Abstract
We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphsim from an appropriately defined graph space to L^2. The results rely on well-posedness and stability of the weak and ultraweak formulation of the second-order wave equation. As an application we define and analyze a space-time least-squares finite element method for solving the wave equation. Some numerical examples for one- and two- dimensional spatial domains are presented.
Keywords
Cite
@article{arxiv.2311.10536,
title = {Well-posedness of first-order acoustic wave equations and space-time finite element approximation},
author = {Thomas Führer and Roberto González and Michael Karkulik},
journal= {arXiv preprint arXiv:2311.10536},
year = {2023}
}