{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T05:54:07Z","timestamp":1785304447179,"version":"3.55.0"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"314","license":[{"start":{"date-parts":[[2019,1,19]],"date-time":"2019-01-19T00:00:00Z","timestamp":1547856000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1114"],"award-info":[{"award-number":["SFB 1114"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1114"],"award-info":[{"award-number":["SFB 1114"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1114"],"award-info":[{"award-number":["SFB 1114"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1114"],"award-info":[{"award-number":["SFB 1114"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present a class of such methods that are closely related to the methods that have recently been proposed by M\u00e5lqvist and Peterseim [Math. Comp. 83, 2014, pp. 2583\u20132603]. Like these methods, the new methods do not make explicit or implicit use of a scale separation. Their comparatively simple analysis is based on the theory of additive Schwarz or subspace decomposition methods.<\/p>","DOI":"10.1090\/mcom\/3302","type":"journal-article","created":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T10:47:55Z","timestamp":1498733275000},"page":"2765-2774","source":"Crossref","is-referenced-by-count":50,"title":["An analysis of a class of variational multiscale methods based on subspace decomposition"],"prefix":"10.1090","volume":"87","author":[{"given":"Ralf","family":"Kornhuber","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Peterseim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Harry","family":"Yserentant","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2018,1,19]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1137\/0720034","article-title":"Generalized finite element methods: their performance and their relation to mixed methods","volume":"20","author":"Babu\u0161ka, I.","year":"1983","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s00211-013-0562-4","article-title":"On the \ud835\udc3b\u00b9-stability of the \ud835\udc3f\u2082-projection onto finite element spaces","volume":"126","author":"Bank, Randolph E.","year":"2014","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"932","DOI":"10.1137\/140991030","article-title":"Low-rank approximation of elliptic boundary value problems with high-contrast coefficients","volume":"48","author":"Bebendorf, Mario","year":"2016","journal-title":"SIAM J. Math. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1410","issn-type":"print"},{"key":"4","isbn-type":"print","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1090\/conm\/180\/01951","article-title":"Two-level additive Schwarz preconditioners for nonconforming finite elements","author":"Brenner, Susanne C.","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0821851713"},{"issue":"4","key":"5","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1137\/0714041","article-title":"Inverses of band matrices and local convergence of spline projections","volume":"14","author":"Demko, Stephen","year":"1977","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"4","key":"6","doi-asserted-by":"publisher","first-page":"1367","DOI":"10.1051\/m2an\/2016066","article-title":"Finite element quasi-interpolation and best approximation","volume":"51","author":"Ern, Alexandre","year":"2017","journal-title":"ESAIM Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/2822-7840","issn-type":"print"},{"key":"7","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-47324-5","volume-title":"Hierarchical matrices: algorithms and analysis","volume":"49","author":"Hackbusch, Wolfgang","year":"2015","ISBN":"https:\/\/id.crossref.org\/isbn\/9783662473238"},{"issue":"5","key":"8","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s00791-013-0211-6","article-title":"Partial evaluation of the discrete solution of elliptic boundary value problems","volume":"15","author":"Hackbusch, Wolfgang","year":"2012","journal-title":"Comput. Vis. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/1432-9360","issn-type":"print"},{"issue":"3","key":"9","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1137\/15M1028510","article-title":"Numerical homogenization of elliptic multiscale problems by subspace decomposition","volume":"14","author":"Kornhuber, Ralf","year":"2016","journal-title":"Multiscale Model. Simul.","ISSN":"https:\/\/id.crossref.org\/issn\/1540-3459","issn-type":"print"},{"issue":"290","key":"10","doi-asserted-by":"publisher","first-page":"2583","DOI":"10.1090\/S0025-5718-2014-02868-8","article-title":"Localization of elliptic multiscale problems","volume":"83","author":"M\u00e5lqvist, Axel","year":"2014","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/BF02243847","article-title":"On a BPX-preconditioner for \ud835\udc431 elements","volume":"51","author":"Oswald, P.","year":"1993","journal-title":"Computing","ISSN":"https:\/\/id.crossref.org\/issn\/0010-485X","issn-type":"print"},{"key":"12","isbn-type":"print","first-page":"341","article-title":"Variational multiscale stabilization and the exponential decay of fine-scale correctors","author":"Peterseim, Daniel","year":"2016","ISBN":"https:\/\/id.crossref.org\/isbn\/9783319416380"},{"issue":"4","key":"13","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1137\/1034116","article-title":"Iterative methods by space decomposition and subspace correction","volume":"34","author":"Xu, Jinchao","year":"1992","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/1095-7200","issn-type":"print"},{"issue":"3-4","key":"14","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s00791-004-0147-y","article-title":"On an energy minimizing basis for algebraic multigrid methods","volume":"7","author":"Xu, Jinchao","year":"2004","journal-title":"Comput. Vis. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/1432-9360","issn-type":"print"},{"key":"15","isbn-type":"print","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1017\/S0962492900002385","article-title":"Old and new convergence proofs for multigrid methods","author":"Yserentant, Harry","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0521443563"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-314\/S0025-5718-2018-03302-6\/mcom3302_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/www.ams.org\/mcom\/2018-87-314\/S0025-5718-2018-03302-6\/S0025-5718-2018-03302-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-314\/S0025-5718-2018-03302-6\/S0025-5718-2018-03302-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:49:14Z","timestamp":1776800954000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2018-87-314\/S0025-5718-2018-03302-6\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,19]]},"references-count":15,"journal-issue":{"issue":"314","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["S0025-5718-2018-03302-6"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3302","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2018,1,19]]}}}