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Radiative heating of a glass plate: the semi-discrete problem (second revision)

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Abstract

In a preceding paper (MSIA, 2012), we have studied the radiative heating of a glass plate. We have proved existence and uniqueness of the solution. Here, we want to study the semi-discrete problem and to prove a priori error estimates. Previously, in that purpose, we have to study the regularity of the solution to the exact problem and of its time derivative. A very important property, Proposition 13, is remarked concerning our elliptic projection, the milestone in deriving the a priori error estimates. A numerical test corroborating our theoretical a priori bounds is given.

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Notes

  1. For convenience the temperatures are cited in \( {{}^\circ }\mathrm{C}\); the corresponding absolute temperatures in \( {{}^\circ }\mathrm{K}\) are obtained by adding 273.15 to the temperatures cited in \( {{}^\circ }\mathrm{C}\).

  2. I take here the opportunity to thank my colleague F. Béchet from the Tempo laboratory in our university, who has made me that remark.

  3. Semi-transparent medium

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Authors and Affiliations

  1. LAMAV-EDP, EA 4015, Institut des Sciences et Techniques de Valenciennes (ISTV2), Univ. Valenciennes, EA 4015-LAMAV, FR CNRS 2956, F-59313, Valenciennes, France

    Luc Paquet

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  1. Luc Paquet
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Correspondence to Luc Paquet.

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Paquet, L. Radiative heating of a glass plate: the semi-discrete problem (second revision). Afr. Mat. 29, 295–330 (2018). https://doi.org/10.1007/s13370-018-0542-z

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  • DOI: https://doi.org/10.1007/s13370-018-0542-z

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