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Computation of eigenvalues by numerical upscaling

Axel Målqvist (Institutionen för matematiska vetenskaper) ; D. Peterseim
Numerische Mathematik (0029-599X). Vol. 130 (2015), 2, p. 337-361.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: FINITE-ELEMENT APPROXIMATION, ELLIPTIC INTERFACE PROBLEMS, A-POSTERIORI, CONVERGENCE



Denna post skapades 2015-06-02. Senast ändrad 2016-01-11.
CPL Pubid: 217915

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

Ämnesområden

Matematik

Chalmers infrastruktur