Finite Element Convergence Analysis For Wave Equations With Time-Dependent Coefficients
Numerical Analysis
2026-03-17 v2 Numerical Analysis
Abstract
Error estimates are proved for finite element approximations to the solution of second-order hyperbolic partial differential equations with coefficients varying in both space and time. Optimal rates of convergence in the energy norm are proved for the semi-discrete Galerkin finite element solution by introducing a time-dependent Ritz-like projection. Numerical experiments corroborate the rates of convergence and illustrate the localized wave field enhancement in a chain of time-modulated subwavelength resonators.
Cite
@article{arxiv.2602.07990,
title = {Finite Element Convergence Analysis For Wave Equations With Time-Dependent Coefficients},
author = {Oussama Al Jarroudi and Marcus J. Grote},
journal= {arXiv preprint arXiv:2602.07990},
year = {2026}
}