Variational Multiscale Finite Element Method for Flows in Highly Porous Media

O. Iliev, R. Lazarov, J. Willems

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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. © 2011 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)1350-1372
Number of pages23
JournalMultiscale Modeling & Simulation
Issue number4
StatePublished - Oct 2011
Externally publishedYes


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