Finite Element Convergence Analysis For Wave Equations With Time-Dependent Coefficients
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.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Stability and Controllability of Differential Equations
Differential Equations and Numerical Methods
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 February 2026
- Language
- EN
- Document type
- Preprint