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Multiscale Mixed Fi...
Multiscale Mixed Finite Elements
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Hellman, Filip, 1984 (author)
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- Henning, Patrick (author)
- KTH,Numerisk analys, NA
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- Målqvist, Axel, 1978 (author)
- Göteborgs universitet,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
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- Hellman, Fredrik (author)
- Uppsala universitet,Avdelningen för beräkningsvetenskap,Numerisk analys
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(creator_code:org_t)
- American Institute of Mathematical Sciences (AIMS), 2016
- 2016
- English.
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In: Discrete and Continuous Dynamical Systems - Series S. - : American Institute of Mathematical Sciences (AIMS). - 1937-1632 .- 1937-1179. ; 9:5, s. 1269-1298
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https://doi.org/10.3...
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- reservoir
- multiscale
- stabilized methods
- Mathematics
- numerical homogenization
- localized orthogonal decomposition
- Mixed finite elements
- upscaling
- elliptic problems
- exterior calculus
- Raviart-Thomas spaces
- simulation
Publication and Content Type
- art (subject category)
- ref (subject category)
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