Multiscale Mixed Finite Elements
Artikel i vetenskaplig tidskrift, 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

Författare

Filip Hellman

P. Henning

Axel Målqvist

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Discrete and Continuous Dynamical Systems - Series S

1937-1632 (ISSN)

Vol. 9 1269-1298

Ämneskategorier

Matematik

DOI

10.3934/dcdss.2016051