Computation of eigenvalues by numerical upscaling
Artikel i vetenskaplig tidskrift, 2015

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 by means of a certain Cl,ment-type quasi-interpolation operator.

CONVERGENCE

ELLIPTIC INTERFACE PROBLEMS

A-POSTERIORI

FINITE-ELEMENT APPROXIMATION

Författare

Axel Målqvist

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Daniel Peterseim

Universität Bonn

Numerische Mathematik

0029-599X (ISSN) 0945-3245 (eISSN)

Vol. 130 2 337-361

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1007/s00211-014-0665-6