A hp-adaptive discontinuous Galerkin method for plasmonic waveguides

Abstract

Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Journal of Computational and Applied Mathematics, 270, November 2014, 10.1016/j.cam.2014.009. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn 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.