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On improved P1-interpolation error estimates in W1,p(0, 1): application to the finite element method.

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Title: On improved P1-interpolation error estimates in W1,p(0, 1): application to the finite element method.
Authors: Chaskalovic, Joel1, Assous, Franck2 assous@ariel.ac.il
Source: Mathematical Modelling & Analysis. 2026, Vol. 31 Issue 1, p96-115. 20p.
Subjects: Finite element method, Error analysis in mathematics, Taylor's series, Mean value theorems, Sobolev spaces, Interpolation
Abstract: Based on a new Taylor-like formula, we derived an improved interpolation error estimate in W1,p. We compare it with the classical error estimates based on the standard Taylor formula, and also with the corresponding interpolation error estimate, derived from the mean value theorem. We then assess the improvement in accuracy we can get from this formula, leading to a significant reduction in finite element computation costs. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Based on a new Taylor-like formula, we derived an improved interpolation error estimate in W1,p. We compare it with the classical error estimates based on the standard Taylor formula, and also with the corresponding interpolation error estimate, derived from the mean value theorem. We then assess the improvement in accuracy we can get from this formula, leading to a significant reduction in finite element computation costs. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3846/mma.2026.22775
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        Text: English
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        PageCount: 20
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      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Error analysis in mathematics
        Type: general
      – SubjectFull: Taylor's series
        Type: general
      – SubjectFull: Mean value theorems
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      – SubjectFull: Sobolev spaces
        Type: general
      – SubjectFull: Interpolation
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      – TitleFull: On improved P1-interpolation error estimates in W1,p(0, 1): application to the finite element method.
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              Text: 2026
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