A hp-adaptive discontinuous Galerkin method for plasmonic waveguides

In this paper we propose and analyse a hp-adaptive discontinuous finite element method for computing electromagnetic modes of propagation supported by waveguide structures comprised of a thin lossy metal film of finite width embedded in an infinite homogeneous dielectric. We propose a goal-oriented or dual weighted residual error estimator based on the solution of a dual problem that we use to drive the adaptive refinement with the aim to compute accurate approximation of the modes. We illustrate in the last section the benefits of the resulting hp-adaptive method in practice, which consist in fast convergence and accurate estimation of the error. We tested the method computing the vanishing modes for a metallic waveguide of square section.