@article{d89c243c4ea9434e862b644a26bf1043,
title = "Variational Multiscale Finite Element Method for Flows in Highly Porous Media",
abstract = "We present a two-scale finite element method (FEM) for solving Brinkman's and Darcy's equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy's equations. In order to reduce the {"}resonance error{"} and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. {\textcopyright} 2011 Society for Industrial and Applied Mathematics.",
author = "O. Iliev and R. Lazarov and J. Willems",
note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: Fraunhofer Institut fur Techno- und Wirtschaftsmathematik, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany, and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113, Sofia, Bulgaria (oleg.iliev@itwm.fraunhofer.de). This author's research was supported by DFG project {"}Multiscale analysis of two-phase flow in porous media with complex heterogeneities.{"}Department of Mathematics, Texas A&M University, College Station, TX 77843, and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113, Sofia, Bulgaria (lazarov@math.tamu.edu). This author's research was supported in parts by award KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST) and by NSF grant DMS-1016525.Department of Mathematics, Texas A&M University, College Station, TX 77843 (jwillems@math.tamu.edu). This author's research was supported by DAAD-PPP D/07/10578, NSF grants DMS-0713829 and DMS-1016525, and the Studienstiftung des deutschen Volkes (German National Academic Foundation). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",
year = "2011",
month = oct,
doi = "10.1137/10079940X",
language = "English (US)",
volume = "9",
pages = "1350--1372",
journal = "Multiscale Modeling & Simulation",
issn = "1540-3459",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}