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Multiscale mixed finite elements
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-6432-5504
2016 (English)In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 9, no 5, 1269-1298 p.Article in journal (Refereed) Published
Abstract [en]

In this work, we propose a mixed finite element method for solving elliptic multiscale problems based on a localized orthogonal decomposition (LOD) of Raviart-Thomas finite element spaces. It requires to solve local problems in small patches around the elements of a coarse grid. These computations can be perfectly parallelized and are cheap to perform. Using the results of these patch problems, we construct a low dimensional multiscale mixed finite element space with very high approximation properties. This space can be used for solving the original saddle point problem in an efficient way. We prove convergence of our approach, independent of structural assumptions or scale separation. Finally, we demonstrate the applicability of our method by presenting a variety of numerical experiments, including a comparison with an MsFEM approach.

Place, publisher, year, edition, pages
2016. Vol. 9, no 5, 1269-1298 p.
Keyword [en]
Mixed finite elements, multiscale, numerical homogenization, Raviart-Thomas spaces, upscaling
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-197783DOI: 10.3934/dcdss.2016051ISI: 000387662300002OAI: oai:DiVA.org:kth-197783DiVA: diva2:1060233
Note

QC 20161228

Available from: 2016-12-28 Created: 2016-12-08 Last updated: 2016-12-28Bibliographically approved

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Henning, Patrick
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