An MsFEM approach enriched using Legendre polynomials

Claude Le Bris; Frederic Legoll; Pierre-Loik Rothe; Ulrich Hetmaniuk

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An MsFEM approach enriched using Legendre polynomials

Frederic Legoll, Pierre-Loik Rothe, Claude Le Bris, Ulrich Hetmaniuk

Numerical Analysis · Submitted 2 Sep 2021

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

The authors' main claim Numerical experiments show a significant reduction in the error at a limited additional off-line cost.

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arXiv ID2109.00990 (version 1)

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CitationClaude Le Bris, Frederic Legoll, Pierre-Loik Rothe, Ulrich Hetmaniuk. "An MsFEM approach enriched using Legendre polynomials." arXiv:2109.00990 (2021). https://pith.science/paper/DT5SDBOU

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,159 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.30 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.59 · mentions code or data availability 0.02.

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We consider a variant of the conventional MsFEM approach with enrichments based on Legendre polynomials, both in the bulk of mesh elements and on their interfaces. A convergence analysis of the approach is presented. Residue-type a posteriori error estimates are also established. Numerical experiments show a significant reduction in the error at a limited additional off-line cost. In particular, the approach developed here is less prone to resonance errors in the regime where the coarse mesh size $H$ is of the order of the small scale $\varepsilon$ of the oscillations.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider a variant of the conventional MsFEM approach with enrichments based on Legendre polynomials, both in the bulk of mesh elements and on their interfaces.	contribution 0.66	0.78	0.06	asserted 0.90
s1	A convergence analysis of the approach is presented.	contribution 0.92	0.92	0.04	asserted 0.96
s2	Residue-type a posteriori error estimates are also established.	contribution 0.87	0.92	0.07	asserted 1.00
s3	Numerical experiments show a significant reduction in the error at a limited additional off-line cost.	result 1.00	0.95	0.48	asserted 1.00
s4	In particular, the approach developed here is less prone to resonance errors in the regime where the coarse mesh size $H$ is of the order of the small scale $\varepsilon$ of the oscillations.	result 0.75	0.91	0.42	asserted 0.98

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.51.

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arXiv listing abstract v1

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Original abstract

We consider a variant of the conventional MsFEM approach with enrichments based on Legendre polynomials, both in the bulk of mesh elements and on their interfaces. A convergence analysis of the approach is presented. Residue-type a posteriori error estimates are also established. Numerical experiments show a significant reduction in the error at a limited additional off-line cost. In particular, the approach developed here is less prone to resonance errors in the regime where the coarse mesh size $H$ is of the order of the small scale $\varepsilon$ of the oscillations.

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Cites as background 1 paper

The approach of [ref] , which is related to domain decomposition methods for elliptic partial differential equations [ref] and to modern component mode synthesis methods [ref] , is very effective.

Analysis of a New Harmonically Enriched Multiscale Coarse Space for Domain Decomposition Methods · Introduction · 0.81

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