Contributions to Books:
"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,
In this paper we deal with holomorphic Fredholm operator eigen-value problems and their approximations by Galerkin schemes. We consider operator functions, which donīt 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.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.