Finite Element Convergence Analysis For Wave Equations With Time-Dependent Coefficients
This work provides theoretical guarantees for finite element methods in wave propagation problems with time-varying coefficients, which is incremental for computational physics and engineering applications.
The paper tackled the problem of proving error estimates for finite element approximations of second-order hyperbolic PDEs with time-dependent coefficients, achieving optimal convergence rates in the energy norm. Numerical experiments confirmed these rates and demonstrated localized wave field enhancement in time-modulated resonators.
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.