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In order to reduce the \u201cresonance error\u201d 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.<\/jats:p>","DOI":"10.1137\/10079940x","type":"journal-article","created":{"date-parts":[[2011,11,2]],"date-time":"2011-11-02T18:13:12Z","timestamp":1320257592000},"page":"1350-1372","source":"Crossref","is-referenced-by-count":39,"title":["Variational Multiscale Finite Element Method for Flows in Highly Porous Media"],"prefix":"10.1137","volume":"9","author":[{"given":"O.","family":"Iliev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Lazarov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Willems","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,11,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375065"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1476(19991110)22:16<1395::AID-MMA84>3.0.CO;2-3"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902406636"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/050631811"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-006-9024-8"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1145\/1268776.1268779"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"J. 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