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Moreover, we show how to stabilize the remaining cases by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments.<\/jats:p>","DOI":"10.1137\/090767029","type":"journal-article","created":{"date-parts":[[2010,3,10]],"date-time":"2010-03-10T18:14:29Z","timestamp":1268244869000},"page":"875-893","source":"Crossref","is-referenced-by-count":51,"title":["A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles"],"prefix":"10.1137","volume":"32","author":[{"given":"L. Beir\u00e3o","family":"da Veiga","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K.","family":"Lipnikov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,10]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/num.20170"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02165003"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-007-0126-6"},{"key":"R4","unstructured":"L. Beir\u00e3o da Veiga,\n                      A mimetic discretization method for linear elasticity\n                      , M2AN Math. Model Numer. Anal., to appear."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.06.034"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-009-0234-6"},{"key":"R7","unstructured":"L. Beir\u00e3o da Veiga, K. Lipnikov, and G. Manzini,\n                      Convergence of the Mimetic Finite Difference Method for the Stokes Problem on Polyhedral Meshes\n                      , Technical report 6PV09\/5\/0, IMATI-CNR, via Ferrata, 1, 27100 Pavia, Italy, 2009, SIAM, J. Numer. Anal., to appear."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2377"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/080717894"},{"key":"R10","first-page":"253","volume":"9","author":"Berndt M.","year":"2001","journal-title":"East-West J. Numer. Math."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/040606831"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2008046"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"F. Brezzi and M. 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Silvester,\n                      Unstable Modes of the ${Q}_1-{P}_0$ Element\n                      , Technical report 257, University of Manchester, Manchester, UK, 1994."},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.06.028"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.2528\/PIER00080104"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.5633"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.02.016"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-008-0203-5"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7225(81)90013-6"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(00)80001-8"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1650110615"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090767029","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:22Z","timestamp":1787334622000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090767029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":35,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090767029"],"URL":"https:\/\/doi.org\/10.1137\/090767029","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}