A posteriori error estimates for finite element discretizations of time-harmonic Maxwell's equations coupled with a non-local hydrodynamic Drude model

TL;DR

This paper develops a residual-based a posteriori error estimator for finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model, enabling efficient mesh adaptivity in simulating localized electromagnetic fields in nanostructures.

Contribution

It introduces a novel reliable and efficient error estimator specifically designed for coupled Maxwell and hydrodynamic Drude models, facilitating adaptive mesh refinement.

Findings

Estimator effectively guides mesh adaptivity

Significant computational savings demonstrated

High accuracy in localized field regions

Abstract

We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error estimation and mesh adaptivity, which is of particular interest since the electromagnetic field usually exhibits strongly localized features near the interface between metals and their surrounding media. We propose a novel residual-based error estimator that is shown to be reliable and efficient. We also present a set of numerical examples where the estimator drives a mesh adaptive process. These examples highlight the quality of the proposed estimator, and the potential computational savings offered by mesh adaptivity.