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A discontinuous least squares finite element method for time-harmonic Maxwell equations

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Ruo Li, Qicheng Liu, Fanyi Yang

Numerical Analysis · Submitted 14 Jul 2020

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

The authors' main claim We prove the convergence orders under both the energy norm and the $L^2$ norm.

how it is stated · asserted 1.00 read the record →

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arXiv ID2007.06791 (version 1)
Pith IDKCOBTWNS, Pith's permanent record of this paper and its review
CitationFanyi Yang, Qicheng Liu, Ruo Li. "A discontinuous least squares finite element method for time-harmonic Maxwell equations." arXiv:2007.06791 (2020). https://pith.science/paper/KCOBTWNS
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,745 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We propose and analyze a discontinuous least squares finite element method for solving the indefinite time-harmonic Maxwell equations. The scheme is based on the $L^2$ norm least squares functional with the weak imposition of the continuity across the interior faces. We minimize the functional over the piecewise polynomial spaces to seek numerical solutions. The method is shown to be stable without any constraint on the mesh size. We prove the convergence orders under both the energy norm and the $L^2$ norm. Numerical results in two and three dimensions are presented to verify the error estimates.

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 We propose and analyze a discontinuous least squares finite element method for solving the indefinite time-harmonic Maxwell equations. contribution 1.00 0.94 0.19 asserted 0.99
s1 The scheme is based on the $L^2$ norm least squares functional with the weak imposition of the continuity across the interior faces. method 0.99 0.82 0.04 asserted 1.00
s2 We minimize the functional over the piecewise polynomial spaces to seek numerical solutions. method 1.00 0.90 0.06 asserted 0.96
s3 The method is shown to be stable without any constraint on the mesh size. result 0.98 0.92 0.22 asserted 1.00
s4 We prove the convergence orders under both the energy norm and the $L^2$ norm. result 0.87 0.95 0.27 asserted 1.00
s5 Numerical results in two and three dimensions are presented to verify the error estimates. result 0.71 0.95 0.11 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.94.

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  • C citations
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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

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Original abstract

We propose and analyze a discontinuous least squares finite element method for solving the indefinite time-harmonic Maxwell equations. The scheme is based on the $L^2$ norm least squares functional with the weak imposition of the continuity across the interior faces. We minimize the functional over the piecewise polynomial spaces to seek numerical solutions. The method is shown to be stable without any constraint on the mesh size. We prove the convergence orders under both the energy norm and the $L^2$ norm. Numerical results in two and three dimensions are presented to verify the error estimates.

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