Volume 53, Number 1, January–February 2019
|Page(s)||301 - 324|
|Published online||15 April 2019|
Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator
College of Mathematics, Sichuan University, Chengdu 610065, P.R. China
2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
3 School of Mathematics Sciences, University of Electronic Science and Technology of China, Sichuan 611731, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 26 January 2019
In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous polynomial approximations. The error analysis is based on a mixed curl-curl formulation for the Maxwell equations. Theoretical results are obtained under a more general regularity requirement. In particular for the low regularity case, special treatment is applied to approximate data on the boundary. The HDG method is shown to be stable and convergence in an optimal order for both high and low regularity cases. Numerical experiments with both smooth and singular analytical solutions are performed to verify the theoretical results.
Mathematics Subject Classification: 65N30
Key words: Maxwell equations / HDG method / low regularity
© EDP Sciences, SMAI 2019
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