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M. Halla:
"Regular Galerkin approximation of holomorphic T-Garding operator eigenvalue problems";
in: "ASC Report 4/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 10.

In this paper we deal with holomorphic Fredholm operator eigen-value problems and their approximations by Galerkin schemes. We consider operator functions, which don´t have the structure "coercive+compact". In this case the regularity (in sense of [O. Karma, Numer. Funct. Anal. Op-tim. 17 (1996)]) of Galerkin approximations is not unconditionally satisfied. We assume that this structure is regained by multiplication with an appropri-ate operator. We analyze in which sense this operator has to be approximable by operators mapping from the Galerkin spaces into themselves in order to en-sure the regularity of Galerkin approximations. We report a sufficient condition which is verifiable in praxis and hence provide a new tool for the numerical analysis of holomorphic Fredholm operator eigenvalue problems.

holomorphic Fredholm operator, non-linear eigenvalue problem, regular approximation, compatible discretization, T-G˚arding.

http://www.asc.tuwien.ac.at/preprint/2016/asc4x2016.pdf