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A space-time FEM for PDEs on evolving surfaces

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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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Joerg Grande, Maxim Olshanskii, Arnold Reusken

Numerical Analysis · Submitted 2 Mar 2014

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

The authors' main claim The numerical method uses space-time finite elements and is provably second order accurate.

how it is stated · asserted 1.00 read the record →

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arXiv ID1403.0277 (version 1)
Pith IDMHS5VXNM, Pith's permanent record of this paper and its review
CitationArnold Reusken, Joerg Grande, Maxim Olshanskii. "A space-time FEM for PDEs on evolving surfaces." arXiv:1403.0277 (2014). https://pith.science/paper/MHS5VXNM
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,765 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.86 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The surface and its evolution may be given implicitly, e.g., as the solution of a level set equation. This approach naturally allows a surface to undergo topological changes and experience local geometric singularities. The numerical method uses space-time finite elements and is provably second order accurate. The paper reviews the method, error estimates and shows results for computing the diffusion of a surfactant on surfaces of two colliding droplets.

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 The paper studies a finite element method for computing transport and diffusion along evolving surfaces. contribution 0.97 0.87 0.11 asserted 1.00
s1 The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. method 0.69 0.62 0.13 asserted 1.00
s2 The surface and its evolution may be given implicitly, e.g., as the solution of a level set equation. method 0.96 0.24 0.04 hedged possibility 0.98
s3 This approach naturally allows a surface to undergo topological changes and experience local geometric singularities. contribution 0.51 0.52 0.13 asserted 0.78
s4 The numerical method uses space-time finite elements and is provably second order accurate. method 0.81 0.91 0.24 asserted 1.00
s5 The paper reviews the method, error estimates and shows results for computing the diffusion of a surfactant on surfaces of two colliding droplets. contribution 0.68 0.93 0.21 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.84.

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
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  • 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

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The surface and its evolution may be given implicitly, e.g., as the solution of a level set equation. This approach naturally allows a surface to undergo topological changes and experience local geometric singularities. The numerical method uses space-time finite elements and is provably second order accurate. The paper reviews the method, error estimates and shows results for computing the diffusion of a surfactant on surfaces of two colliding droplets.

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