A mixed method for time-transient acoustic wave propagation in metamaterials

TL;DR

This paper develops a finite element method for simulating time-dependent acoustic wave propagation in Drude-type metamaterials, providing theoretical error analysis and numerical validation.

Contribution

It introduces a mixed finite element approach combined with Crank-Nicolson time discretization for modeling wave propagation in metamaterials, with detailed error analysis.

Findings

The method accurately simulates wave propagation in metamaterials.

Theoretical error bounds are established for the numerical scheme.

Numerical experiments confirm the effectiveness of the approach.

Abstract

In this paper we develop a finite element method for acoustic wave propagation in Drude-type metamaterials. The governing equation is written as a symmetrizable hyperbolic system with auxiliary variables. The standard mixed finite elements and discontinuous finite elements are used for spatial discretization, and the Crank-Nicolson scheme is used for time discretization. The a priori error analysis of fully discrete scheme is carried out in details. Numerical experiments illustrating the theoretical results and metamaterial wave propagation, are included.