An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications

Giani, S.

Abstract

In this paper we propose and analyse an error estimator suitable for \(hp\)-adaptive continuous finite element methods for computing the band structure and the isolated modes of 2D photonic crystal (PC) applications. The error estimator that we propose is based on the residual of the discrete problem and we show that it leads to very fast convergence in all considered examples when used with \(hp\)-adaptive refinement techniques. In order to show the flexibility and robustness of the error estimator we present an extensive collection of numerical experiments inspired by real applications. In particular we are going to consider PCs with point defects, PCs with line defects, bended waveguides and semi-infinite PCs.

Citation

Giani, S. (2013). An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications. Computing, 95(5), 395-414. https://doi.org/10.1007/s00607-012-0244-6

• Journal Article Type: Article
• Acceptance Date: Nov 16, 2012
• Publication Date: May 1, 2013
• Deposit Date: Feb 12, 2013
• Publicly Available Date: Oct 13, 2015
• Journal: Computing
• Print ISSN: 0010-485X
• Electronic ISSN: 1436-5057
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Issue: 5
• Pages: 395-414
• DOI: https://doi.org/10.1007/s00607-012-0244-6
• Keywords: Eigenvalue problem, Finite element method, hp-adaptivity, A posteriori error estimator, Photonic crystals.