Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales

Author: Assyr Abdulle
Journal: Math. Comp. 81 (2012), 687-713
MSC (2010): Primary 65N30, 65M60; Secondary 74Q05, 35J15
Posted: July 26, 2011
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Abstract: An analysis of a multiscale symmetric interior penalty discontinuous Galerkin finite element method for the numerical discretization of elliptic problems with multiple scales is proposed. This new method, first described in [A. Abdulle, C.R. Acad. Sci. Paris, Ser. I 346 (2008)] is based on numerical homogenization. It allows to significantly reduce the computational cost of a fine scale discontinuous Galerkin method by probing the fine scale data on sampling domains within a macroscopic partition of the computational domain. Macroscopic numerical fluxes, an essential ingredient of discontinuous Galerkin finite elements, can be recovered from the computation on the sampling domains with negligible computation overhead. Fully discrete a priori error bounds are derived in the and norms.

References

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