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Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator

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Gang Chen, Jintao Cui, Liwei Xu

Numerical Analysis · Submitted 23 May 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The HDG method is shown to be stable and convergence in an optimal order for both high and low regularity cases.

how it is stated · asserted 1.00 read the record →

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arXiv ID1805.09291 (version 4)
Pith ID4HPJOQO4, Pith's permanent record of this paper and its review
CitationGang Chen, Jintao Cui, Liwei Xu. "Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator." arXiv:1805.09291 (2018). https://pith.science/paper/4HPJOQO4
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,429 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. contribution 0.98 0.89 0.05 asserted 0.87
s1 The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous polynomial approximations. method 0.99 0.51 0.04 asserted 1.00
s2 The error analysis is based on a mixed curl-curl formulation for the Maxwell equations. method 0.98 0.81 0.03 asserted 1.00
s3 Theoretical results are obtained under a more general regularity requirement. contribution 0.57 0.88 0.05 asserted 1.00
s4 In particular for the low regularity case, special treatment is applied to approximate data on the boundary. method 0.91 0.91 0.03 asserted 1.00
s5 The HDG method is shown to be stable and convergence in an optimal order for both high and low regularity cases. result 1.00 0.94 0.82 asserted 1.00
s6 Numerical experiments with both smooth and singular analytical solutions are performed to verify the theoretical results. method 0.70 0.96 0.06 asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.54 · evidence from proof or derivation 0.98.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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.

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