English

An absolutely stable $hp$-HDG method for the time-harmonic Maxwell equations with high wave number

Numerical Analysis 2016-01-21 v3

Abstract

We present and analyze a hybridizable discontinuous Galerkin (HDG) method for the time-harmonic Maxwell equations. The divergence-free condition is enforced on the electric field, then a Lagrange multiplier is introduced, and the problem becomes the solution of a mixed curl-curl formulation of the Maxwell's problem. The method is shown to be an absolutely stable HDG method for the indefinite time-harmonic Maxwell equations with high wave number. By exploiting the duality argument, the dependence of convergence of the HDG method on the wave number k, the mesh size h and the polynomial order p is obtained. Numerical results are given to verify the theoretical analysis.

Keywords

Cite

@article{arxiv.1503.07696,
  title  = {An absolutely stable $hp$-HDG method for the time-harmonic Maxwell equations with high wave number},
  author = {Peipei Lu and Huangxin Chen and Weifeng Qiu},
  journal= {arXiv preprint arXiv:1503.07696},
  year   = {2016}
}