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 div σ∇u = f set in H1 0 , with σ exhibiting a sign change.