Work

Multiscale method based on discontinuous Galerkin methods for homogenization problems

Year: 2007

Type: article

Abstract: We propose a multiscale method for elliptic problems with highly oscillating coefficients based on a coupling of macro and micro methods in the framework of the heterogeneous multiscale method. The macro method, defined on a macroscopic triangulation, aims at recovering the effective (homogenized) solution of an unknown macro model. The unspecified data of this model are computed by micro methods on sampling domains during the macro assembly process. In this Note, we show how to construct such a coupling with a discontinuous macro finite element space. We show that the flux information needed in this formulation in order to impose weak interelement continuity can be recovered from the known micro calculations on the sampling domains. A fully discrete analysis is presented.

Source: Comptes Rendus Mathématique

DOI: 10.1016/j.crma.2007.11.029

Author: Assyr Abdulle

Institutions: Maxwell Institute for Mathematical Sciences, University of Edinburgh

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funder: Engineering and Physical Sciences Research Council

Award: Multiscale methods for nonlinear problems in strongly heterogeneous media and stiff stochastic systems