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Afrika Matematika

, Volume 29, Issue 1–2, pp 295–330 | Cite as

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

  • Luc Paquet
Article
  • 37 Downloads

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.

Keywords

Planck function Radiative heat flux in a glass plate Nonlinear heat-conduction equation Regularity of the exact solution and of its time derivative Semi-discrete problem Elliptic projection A priori error estimates 

Mathematics Subject Classification

35K20 35K55 45K05 65M22 65M60 65M15 

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.LAMAV-EDP, EA 4015, Institut des Sciences et Techniques de Valenciennes (ISTV2)Univ. ValenciennesValenciennesFrance

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