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Multiscale Mixed Finite Elements

Filip Hellman ; P. Henning ; Axel Målqvist (Institutionen för matematiska vetenskaper, matematik)
Discrete and Continuous Dynamical Systems-Series S (1937-1632). Vol. 9 (2016), 5, p. 1269-1298.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Mixed finite elements, multiscale, numerical homogenization, Raviart-Thomas spaces, upscaling, localized orthogonal decomposition, elliptic problems, reservoir, simulation, stabilized methods, exterior calculus, Mathematics

Denna post skapades 2016-12-09.
CPL Pubid: 246015


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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