Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibility

Abstract We consider Galerkin approximations of eigenvalue problems for holomorphic Fredholm operator functions which the operators do not have structure “coercive+compact”. In this case regularity (in vocabulary discrete approximation schemes ) is unconditionally satisfied and question convergence delicate. report a technique to prove applicable wide range problems. The based on knowledge suitable T est function operator. particular, we introduce concepts weak T-coercivity T-compatibility that weakly T-coercive operators, implies their regularity. Our framework can be successfully applied analyze e.g. complex scaling/perfectly matched layer methods, involving sign-changing coefficients due meta-materials also (boundary element) Maxwell-type equations. demonstrate application our Maxwell problem conductive material.