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Numerische Mathematik

, Volume 90, Issue 4, pp 775–786 | Cite as

On a generalized $L_2$ projection and some related stability estimates in Sobolev spaces

  • Olaf Steinbach
Original article

Summary.

In this paper we investigate a stability estimate needed in hybrid finite and boundary element methods, especially in hybrid coupled domain decomposition methods including mortar finite elements. This stability estimate is equivalent to the stability of a generalized \(L_2\) projection in certain Sobolev spaces. Using piecewise linear trial spaces and appropriate piecewise constant test spaces, the stability of the generalized \(L_2\) projection is proved assuming some mesh conditions locally.

Mathematics Subject Classification (1991):65D05, 65N30, 65N50 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Olaf Steinbach
    • 1
  1. 1.Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany; e-mail: steinbach@mathematik.uni-stuttgart.de DE

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