{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:22:44Z","timestamp":1758709364492},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p> We propose and analyze several two-level non-overlapping Schwarz methods\nfor a preconditioned weakly over-penalized symmetric interior penalty (WOPSIP)\ndiscretization of a second order boundary value problem. We show that the preconditioners\nare scalable and that the condition number of the resulting preconditioned\nlinear systems of equations is independent of the penalty parameter and is of order\n<jats:bold>H\/h<\/jats:bold>, where <jats:bold>H<\/jats:bold> and <jats:bold>h<\/jats:bold> represent the mesh sizes of the coarse and fine partitions, respectively.\nNumerical experiments that illustrate the performance of the proposed two-level Schwarz methods are also presented.<\/jats:p>","DOI":"10.2478\/cmam-2012-0021","type":"journal-article","created":{"date-parts":[[2013,2,13]],"date-time":"2013-02-13T12:23:49Z","timestamp":1360758229000},"page":"241-272","source":"Crossref","is-referenced-by-count":12,"title":["Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems"],"prefix":"10.2478","volume":"12","author":[{"given":"Paola F.","family":"Antonietti","sequence":"first","affiliation":[{"name":"1MOX--Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leondardo da Vinci 32, 20133 Milano, Italy."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Blanca","family":"Ayuso de Dios","sequence":"additional","affiliation":[{"name":"2Centre de Recerca Matem\u00e1tica, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Susanne C.","family":"Brenner","sequence":"additional","affiliation":[{"name":"3Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li-yeng","family":"Sung","sequence":"additional","affiliation":[{"name":"3Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/12\/3\/article-p241.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2012-0021\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:22:28Z","timestamp":1619101348000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/12\/3\/article-p241.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2012-0021","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}