Multiscale Mixed Finite Elements
Journal article, 2016
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.
reservoir
multiscale
stabilized methods
Mathematics
numerical homogenization
localized orthogonal decomposition
Mixed finite elements
upscaling
elliptic problems
exterior calculus
Raviart-Thomas spaces
simulation
Author
Filip Hellman
P. Henning
Axel Målqvist
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Discrete and Continuous Dynamical Systems - Series S
1937-1632 (ISSN) 19371179 (eISSN)
Vol. 9 5 1269-1298Subject Categories
Mathematics
DOI
10.3934/dcdss.2016051