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On the approximation of linear elliptic systems on polygonal domains

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1121)

Abstract

Least squares approximations of first order systems are considered for a model problem. In the presence of corner singularities the convergence may become arbitrarily slow for increasing inner angles. For non-convex polygonal domains the method is even divergent.

For improvement, the method of dual singular functions (DSFM) is proposed. In the DSFM the approximating spaces are augmented by singular functions of the continuous problem. The so-called stress intensity factors (SIF) are approximated by means of an integral representation formula which is obtained using the singular functions of the adjoint problem. Here, the solution and the SIF are calculated with the same rates as is done by the non-modified method for the regular part of the solution. Finally, in some numerical examples the DSFM is compared with the wellknown singular function method.

Keywords

  • Stress Intensity Factor
  • Stress Intensity Factor
  • Regular Part
  • Finite Element Approximation
  • Optimal Convergence

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1985 Springer-Verlag

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Blum, H. (1985). On the approximation of linear elliptic systems on polygonal domains. In: Grisvard, P., Wendland, W.L., Whiteman, J.R. (eds) Singularities and Constructive Methods for Their Treatment. Lecture Notes in Mathematics, vol 1121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076260

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  • DOI: https://doi.org/10.1007/BFb0076260

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15219-4

  • Online ISBN: 978-3-540-39377-1

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