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Mathematics > Numerical Analysis

arXiv:1501.05526 (math)
[Submitted on 22 Jan 2015 (v1), last revised 20 Jun 2016 (this version, v3)]

Title:Multiscale mixed finite elements

Authors:Fredrik Hellman, Patrick Henning, Axel Målqvist
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Abstract: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.
Subjects: Numerical Analysis (math.NA)
MSC classes: 35J15, 35M10, 65N12, 65N30, 76S05
Cite as: arXiv:1501.05526 [math.NA]
  (or arXiv:1501.05526v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1501.05526

Submission history

From: Fredrik Hellman [view email]
[v1] Thu, 22 Jan 2015 15:05:59 UTC (391 KB)
[v2] Fri, 24 Jul 2015 14:36:36 UTC (2,015 KB)
[v3] Mon, 20 Jun 2016 14:22:02 UTC (2,015 KB)
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