Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics

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FINITE ELEMENT MULTISCALE METHODS FOR POISSON’S EQUATION WITH RAPIDLY VARYING HETEROGENEOUS COEFFICIENTS

Elfverson, D. ; Malqvist, A. ;

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An abstract framework for constructing finite element multiscale methods is presented. Using this framework we propose and compare two different multiscale methods, one based on the continuous Galerkin finite element method and one on the discontinuous Galerkin finite element method. In these multiscale methods the solution is split into coarse and fine scale contributions. The fine scale contribution is obtained by solving localized constituent problems on patches and is used to obtain a modified coarse scale equation. The localized constituent problems are completely parallelizable i.e, no communication between the different problems are needed. The modified coarse scale equation has considerably less degrees of freedom than the original problem. Numerical experiments are presented where the effect of the patch size of the local constituent problems as well as the convergence of the multiscale methods are investigated and compared for the proposed multiscale methods. We conclude that for a given accuracy and a fixed number of patches, smaller patches can be used for the discontinuous Galerkin multiscale method compared to the continuous Galerkin multiscale method.

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Palavras-chave: finite element methods, discontinuous Galerkin, multiscale methods,

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DOI: 10.5151/meceng-wccm2012-18132

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Como citar:

Elfverson, D.; Malqvist, A.; "FINITE ELEMENT MULTISCALE METHODS FOR POISSON’S EQUATION WITH RAPIDLY VARYING HETEROGENEOUS COEFFICIENTS", p. 836-845 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18132

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