Numerische Mathematik

, Volume 130, Issue 2, pp 337–361 | Cite as

Computation of eigenvalues by numerical upscaling

Article

Abstract

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 \(\text {H}^1_0(\Omega )\) by means of a certain Clément-type quasi-interpolation operator.

Mathematics Subject Classification

65N30 65N25 65N15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesChalmers University of Technology and University of GothenburgGöteborgSweden
  2. 2.Institute for Numerical SimulationRheinische Friedrich-Wilhelms-Universität BonnBonnGermany

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