{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T03:15:16Z","timestamp":1777864516843,"version":"3.51.4"},"reference-count":8,"publisher":"American Mathematical Society (AMS)","issue":"267","license":[{"start":{"date-parts":[[2009,9,25]],"date-time":"2009-09-25T00:00:00Z","timestamp":1253836800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We introduce a method for treating general boundary conditions in the finite element method generalizing an approach, due to Nitsche (1971), for approximating Dirichlet boundary conditions. We use Poisson\u2019s equations as a model problem and prove a priori and a posteriori error estimates. The method is also compared with the traditional Galerkin method. The theoretical results are verified numerically.<\/p>","DOI":"10.1090\/s0025-5718-08-02183-2","type":"journal-article","created":{"date-parts":[[2009,4,27]],"date-time":"2009-04-27T13:47:33Z","timestamp":1240840053000},"page":"1353-1374","source":"Crossref","is-referenced-by-count":150,"title":["Nitsche\u2019s method for general boundary conditions"],"prefix":"10.1090","volume":"78","author":[{"given":"Mika","family":"Juntunen","sequence":"first","affiliation":[]},{"given":"Rolf","family":"Stenberg","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,9,25]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1137\/S0036142901384162","article-title":"Unified analysis of discontinuous Galerkin methods for elliptic problems","volume":"39","author":"Arnold, Douglas N.","year":"2001","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492902000090","article-title":"Survey of meshless and generalized finite element methods: a unified approach","volume":"12","author":"Babu\u0161ka, Ivo","year":"2003","journal-title":"Acta Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0962-4929","issn-type":"print"},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1051\/m2an:2003023","article-title":"A finite element method for domain decomposition with non-matching grids","volume":"37","author":"Becker, Roland","year":"2003","journal-title":"M2AN Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"issue":"6","key":"4","doi-asserted-by":"publisher","first-page":"2431","DOI":"10.1137\/S0036142994264079","article-title":"A posteriori error estimators for the Raviart-Thomas element","volume":"33","author":"Braess, D.","year":"1996","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"5","series-title":"Studies in Mathematics and its Applications, Vol. 4","isbn-type":"print","volume-title":"The finite element method for elliptic problems","author":"Ciarlet, Philippe G.","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0444850287"},{"key":"6","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/BF02995904","article-title":"\u00dcber ein Variationsprinzip zur L\u00f6sung von Dirichlet-Problemen bei Verwendung von Teilr\u00e4umen, die keinen Randbedingungen unterworfen sind","volume":"36","author":"Nitsche, J.","year":"1971","journal-title":"Abh. Math. Sem. Univ. Hamburg","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5858","issn-type":"print"},{"key":"7","isbn-type":"print","first-page":"CD-ROM file","article-title":"Mortaring by a method of J. A. Nitsche","author":"Stenberg, Rolf","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/8489925151"},{"key":"8","unstructured":"R\u00fcdiger Verf\u00fcrth, A review of a posteriori error estimation and adaptive mesh refinement techniques, Wiley, 1996."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-08-02183-2\/S0025-5718-08-02183-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-08-02183-2\/S0025-5718-08-02183-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:07:45Z","timestamp":1776787665000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-08-02183-2\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,25]]},"references-count":8,"journal-issue":{"issue":"267","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["S0025-5718-08-02183-2"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-08-02183-2","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":[[2008,9,25]]}}}