Numerische Mathematik

, Volume 124, Issue 1, pp 1–29 | Cite as

T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients



To solve variational indefinite problems, one uses classically the Banach–Nečas–Babuška theory. Here, we study an alternate theory to solve those problems: T-coercivity. Moreover, we prove that one can use this theory to solve the approximate problems, which provides an alternative to the celebrated Fortin lemma. We apply this theory to solve the indefinite problem \(\text{ div}\sigma \nabla u=f\) set in \(H^1_0\), with \(\sigma \) exhibiting a sign change.

Mathematics Subject Classification

65N30 78A48 35J20 35B65 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Laboratoire POEMS, UMR 7231 CNRS/ENSTA/INRIAENSTA ParisTechPalaiseau CedexFrance

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