Numerische Mathematik

, Volume 126, Issue 4, pp 589–633 | Cite as

Discontinuous Galerkin finite element heterogeneous multiscale method for advection–diffusion problems with multiple scales

Article

Abstract

A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advection–diffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advection–diffusion problem on a macroscopic mesh, whose a priori unknown data are recovered from micro finite element calculations on sampling domains within each macro element. The computational work involved is independent of the high oscillations in the problem at the smallest scale. The stability of our method (depending on both macro and micro mesh sizes) is established for both diffusion dominated and advection dominated regimes without any assumptions about the type of heterogeneities in the data. Fully discrete a priori error bounds are derived for locally periodic data. Numerical experiments confirm the theoretical error estimates.

Mathematics Subject Classification (2010)

65N12 65N15 65N3 74Q05 

Notes

Acknowledgments

This work was supported in part by the Swiss National Science Foundation under Grant 200021 134716/1.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.ANMC, Mathematics SectionÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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