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Virtual Elements on polyhedra with a curved face

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Franco Brezzi, L. Donatella Marini

Numerical Analysis · Submitted 12 May 2023

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

The authors' main claim The new approach looks promising, although sound numerical tests should be made to validate the efficiency of the method.

how it is stated · hedged possibility 0.83 read the record →

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arXiv ID2305.07449 (version 1)
Pith IDBAHZXJEO, Pith's permanent record of this paper and its review
CitationFranco Brezzi, L. Donatella Marini. "Virtual Elements on polyhedra with a curved face." arXiv:2305.07449 (2023). https://pith.science/paper/BAHZXJEO
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,529 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.94 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.33 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we introduce a couple of new ideas for the construction of VEM-approximations on domains with curved boundary, both in two and three dimensions. The new approach looks promising, although sound numerical tests should be made to validate the efficiency of the method.

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 revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. background 0.96 0.50 0.03 asserted 0.78
s1 We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. background 1.00 0.12 0.02 asserted 0.93
s2 In the second part of the paper we introduce a couple of new ideas for the construction of VEM-approximations on domains with curved boundary, both in two and three dimensions. contribution 1.00 0.89 0.12 asserted 1.00
s3 The new approach looks promising, although sound numerical tests should be made to validate the efficiency of the method. limitation 0.49 0.25 0.40 hedged possibility 0.83

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from argument 0.65.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we introduce a couple of new ideas for the construction of VEM-approximations on domains with curved boundary, both in two and three dimensions. The new approach looks promising, although sound numerical tests should be made to validate the efficiency of the method.

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