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Numerical methods for elliptic partial differential equations with rapidly oscillating coefficients

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Title: Numerical methods for elliptic partial differential equations with rapidly oscillating coefficients
Authors: Conca, C.1 cconca@dim.uchile.cl, Natesan, S.2 natesan@dim.uchile.cl
Source: Computer Methods in Applied Mechanics & Engineering. Jan2003, Vol. 192 Issue 1/2, p47. 30p.
Subjects: Elliptic operators, Numerical analysis
Abstract: This paper presents two methods for the numerical solution of the classical homogenization problem of elliptic operators with periodically oscillating coefficients. The numerical solution of such problems is difficult because of the presence of rapidly oscillating coefficients. The first method based on the classical one which consists of the homogenized solution, the first- and second-order correctors, whereas the second one is based on the Bloch wave approach. Further, for the calculation of the homogenized coefficients and some auxiliary functions involved in this method, we applied both methods and compared their accuracies. The Bloch approximation consists in determining an oscillating integral, numerically. The Bloch method provides a better approximation to the exact solution than the classical first-order corrector term in the smooth coefficients case. Moreover, we provided Taylor approximations for the Bloch approximation function and implemented it numerically. In order to show the efficiency of these methods, exhaustive numerical examples in both one and two-dimensional cases are presented. [Copyright &y& Elsevier]
Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. 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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An: 8806754
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  Data: Numerical methods for elliptic partial differential equations with rapidly oscillating coefficients
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  Data: <searchLink fieldCode="AR" term="%22Conca%2C+C%2E%22">Conca, C.</searchLink><relatesTo>1</relatesTo><i> cconca@dim.uchile.cl</i><br /><searchLink fieldCode="AR" term="%22Natesan%2C+S%2E%22">Natesan, S.</searchLink><relatesTo>2</relatesTo><i> natesan@dim.uchile.cl</i>
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  Data: <searchLink fieldCode="JN" term="%22Computer+Methods+in+Applied+Mechanics+%26+Engineering%22">Computer Methods in Applied Mechanics & Engineering</searchLink>. Jan2003, Vol. 192 Issue 1/2, p47. 30p.
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  Data: This paper presents two methods for the numerical solution of the classical homogenization problem of elliptic operators with periodically oscillating coefficients. The numerical solution of such problems is difficult because of the presence of rapidly oscillating coefficients. The first method based on the classical one which consists of the homogenized solution, the first- and second-order correctors, whereas the second one is based on the Bloch wave approach. Further, for the calculation of the homogenized coefficients and some auxiliary functions involved in this method, we applied both methods and compared their accuracies. The Bloch approximation consists in determining an oscillating integral, numerically. The Bloch method provides a better approximation to the exact solution than the classical first-order corrector term in the smooth coefficients case. Moreover, we provided Taylor approximations for the Bloch approximation function and implemented it numerically. In order to show the efficiency of these methods, exhaustive numerical examples in both one and two-dimensional cases are presented. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. 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: 10.1016/S0045-7825(02)00500-5
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      – Code: eng
        Text: English
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        PageCount: 30
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        Type: general
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      – TitleFull: Numerical methods for elliptic partial differential equations with rapidly oscillating coefficients
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              Text: Jan2003
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              Y: 2003
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