Localization of elliptic multiscale problems
Journal article, 2014

This paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches. Hence, on a uniform mesh of size $ H$, patches of diameter $ H\log (1/H)$ are sufficient to preserve a linear rate of convergence in $ H$ without pre-asymptotic or resonance effects. The analysis does not rely on regularity of the solution or scale separation in the coefficient. This result motivates new and justifies old classes of variational multiscale methods. - See more at: http://www.ams.org/journals/mcom/2014-83-290/S0025-5718-2014-02868-8/#sthash.z2CCFXIg.dpuf

multiscale method

Finite element method

a priori error estimate



Axel Målqvist

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Daniel Peterseim

Mathematics of Computation

0025-5718 (ISSN) 1088-6842 (eISSN)

Vol. 83 290 2583-2603

Subject Categories


Computational Mathematics



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