%0 Journal Article
%T Computation of eigenvalues by numerical upscaling
%A Axel Malqvist
%A Daniel Peterseim
%J Mathematics
%D 2012
%I arXiv
%X We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we consider benchmark multi-scale eigenvalue problems in reservoir modeling and material science. We compute a low-dimensional generalized (possibly mesh free) finite element space that preserves the lowermost eigenvalues in a superconvergent way. The approximate eigenpairs are then obtained by solving the corresponding low-dimensional algebraic eigenvalue problem. The rigorous error bounds are based on two-scale decompositions of $H^1_0(\Omega)$ by means of a certain Cl\'ement-type quasi-interpolation operator.
%U http://arxiv.org/abs/1212.0090v3