A Superconvergent HDG Method for the Maxwell Equations

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

30 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)1010-1029
Journal / PublicationJournal of Scientific Computing
Volume70
Issue number3
Online published24 Aug 2016
Publication statusPublished - Mar 2017

Abstract

We present and analyze a new hybridizable discontinuous Galerkin (HDG) method for the steady state Maxwell equations. In order to make the problem well-posed, a condition of divergence is imposed on the electric field. Then a Lagrange multiplier p is introduced, and the problem becomes the solution of a mixed curl–curl formulation of the Maxwell’s problem. We use polynomials of degree + 1 , k, k to approximate u, ∇ × u and p respectively. In contrast, we only use a non-trivial subspace of polynomials of degree + 1 to approximate the numerical tangential trace of the electric field and polynomials of degree + 1 to approximate the numerical trace of the Lagrange multiplier on the faces. On the simplicial meshes, we show that the convergence rates for u and ∇ × u are independent of the Lagrange multiplier p. If we assume the dual operator of the Maxwell equation on the domain has adequate regularity, we show that the convergence rate for u is O(hk+2). From the point of view of degrees of freedom of the globally coupled unknown: numerical trace, this HDG method achieves superconvergence for the electric field without postprocessing. Finally, we show that the superconvergence of the HDG method is also derived on general polyhedral elements. Numerical results are given to verify the theoretical analysis.

Research Area(s)

  • Discontinuous Galerkin, General polyhedral mesh, Hybridization, Maxwell equations, Simplicial mesh, Superconvergence

Citation Format(s)

A Superconvergent HDG Method for the Maxwell Equations. / Chen, Huangxin; Qiu, Weifeng; Shi, Ke et al.
In: Journal of Scientific Computing, Vol. 70, No. 3, 03.2017, p. 1010-1029.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review