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On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems

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Svetlana Matculevich, Monika Wolfmayr

Numerical Analysis · Submitted 25 Mar 2018

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

The authors' main claim The numerical results confirm the reliability and efficiency of the error estimates derived.

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arXiv ID1803.09232 (version 2)
Pith IDA2PTK2UE, Pith's permanent record of this paper and its review
CitationMonika Wolfmayr, Svetlana Matculevich. "On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems." arXiv:1803.09232 (2018). https://pith.science/paper/A2PTK2UE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,583 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.03 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.07 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.

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 This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. contribution 0.95 0.78 0.08 asserted 0.94
s1 We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). contribution 0.67 0.96 0.15 asserted 1.00
s2 Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. contribution 0.82 0.95 0.05 asserted 0.98
s3 The numerical results confirm the reliability and efficiency of the error estimates derived. result 0.81 0.94 0.77 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.69 · evidence from proof or derivation 0.64.

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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

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.

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