{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T12:29:53Z","timestamp":1778588993960,"version":"3.51.4"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"302","license":[{"start":{"date-parts":[[2017,1,14]],"date-time":"2017-01-14T00:00:00Z","timestamp":1484352000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-12-1-0399"],"award-info":[{"award-number":["FA9550-12-1-0399"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["NSF-DMS 1216356"],"award-info":[{"award-number":["NSF-DMS 1216356"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["FA9550-12-1-0399"],"award-info":[{"award-number":["FA9550-12-1-0399"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["NSF-DMS 1216356"],"award-info":[{"award-number":["NSF-DMS 1216356"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The existence of uniformly bounded discrete extension operators is established for conforming Raviart-Thomas and N\u00e9delec discretizations of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H left-parenthesis d i v right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mi>i<\/mml:mi>\n                            <mml:mi>v<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">H(div)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H left-parenthesis c u r l right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:mi>u<\/mml:mi>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mi>l<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">H(curl)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    on locally refined partitions of a polyhedral domain into tetrahedra.\n                  <\/p>","DOI":"10.1090\/mcom\/3074","type":"journal-article","created":{"date-parts":[[2015,10,21]],"date-time":"2015-10-21T10:08:33Z","timestamp":1445422113000},"page":"2639-2650","source":"Crossref","is-referenced-by-count":10,"title":["Discrete extension operators for mixed finite element spaces on locally refined meshes"],"prefix":"10.1090","volume":"85","author":[{"given":"Mark","family":"Ainsworth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Johnny","family":"Guzm\u00e1n","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco-Javier","family":"Sayas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2016,1,14]]},"reference":[{"issue":"226","key":"1","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1090\/S0025-5718-99-01013-3","article-title":"An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations","volume":"68","author":"Alonso, Ana","year":"1999","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"6","key":"2","doi-asserted-by":"publisher","first-page":"1901","DOI":"10.1137\/S0036142997330809","article-title":"The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling","volume":"36","author":"Ainsworth, Mark","year":"1999","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/PL00005386","article-title":"Multigrid in \ud835\udc3b(\ud835\udc51\ud835\udc56\ud835\udc63) and \ud835\udc3b(\ud835\udc50\ud835\udc62\ud835\udc5f\ud835\udc59)","volume":"85","author":"Arnold, Douglas N.","year":"2000","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1002\/num.10040","article-title":"On the mixed finite element method with Lagrange multipliers","volume":"19","author":"Babu\u0161ka, Ivo","year":"2003","journal-title":"Numer. Methods Partial Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0749-159X","issn-type":"print"},{"key":"5","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36519-5","volume-title":"Mixed finite element methods and applications","volume":"44","author":"Boffi, Daniele","year":"2013","ISBN":"https:\/\/id.crossref.org\/isbn\/9783642365188"},{"issue":"1","key":"6","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1002\/1099-1476(20010110)24:1<9::AID-MMA191>3.0.CO;2-2","article-title":"On traces for functional spaces related to Maxwell\u2019s equations. I. An integration by parts formula in Lipschitz polyhedra","volume":"24","author":"Buffa, A.","year":"2001","journal-title":"Math. Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0170-4214","issn-type":"print"},{"issue":"1","key":"7","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1002\/1099-1476(20010110)24:1<9::AID-MMA191>3.0.CO;2-2","article-title":"On traces for functional spaces related to Maxwell\u2019s equations. II. Hodge decompositions on the boundary of Lipschitz polyhedra and applications","volume":"24","author":"Buffa, A.","year":"2001","journal-title":"Math. Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0170-4214","issn-type":"print"},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1016\/S0022-247X(02)00455-9","article-title":"On traces for \ud835\udc3b(\ud835\udc50\ud835\udc62\ud835\udc5f\ud835\udc59,\u03a9) in Lipschitz domains","volume":"276","author":"Buffa, A.","year":"2002","journal-title":"J. Math. Anal. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-247X","issn-type":"print"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/BF01396752","article-title":"Mixed finite elements for second order elliptic problems in three variables","volume":"51","author":"Brezzi, Franco","year":"1987","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"262","key":"10","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1090\/S0025-5718-07-02081-9","article-title":"Smoothed projections in finite element exterior calculus","volume":"77","author":"Christiansen, Snorre H.","year":"2008","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":"227","DOI":"10.1007\/BF01204238","article-title":"Neumann and mixed problems on curvilinear polyhedra","volume":"15","author":"Dauge, Monique","year":"1992","journal-title":"Integral Equations Operator Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0378-620X","issn-type":"print"},{"issue":"6","key":"12","doi-asserted-by":"publisher","first-page":"3006","DOI":"10.1137\/070698786","article-title":"Polynomial extension operators. I","volume":"46","author":"Demkowicz, Leszek","year":"2008","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"12","key":"13","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1016\/j.crma.2003.10.025","article-title":"Stability of discrete liftings","volume":"337","author":"Dom\u00ednguez, V\u00edctor","year":"2003","journal-title":"C. R. Math. Acad. Sci. Paris","ISSN":"https:\/\/id.crossref.org\/issn\/1631-073X","issn-type":"print"},{"issue":"276","key":"14","doi-asserted-by":"publisher","first-page":"1911","DOI":"10.1090\/S0025-5718-2011-02466-X","article-title":"Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem","volume":"80","author":"Gatica, Gabriel N.","year":"2011","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"15","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/s10543-012-0369-1","article-title":"Stable multilevel splittings of boundary edge element spaces","volume":"52","author":"Hiptmair, Ralf","year":"2012","journal-title":"BIT","ISSN":"https:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"},{"issue":"296","key":"16","doi-asserted-by":"publisher","first-page":"2589","DOI":"10.1090\/mcom\/2955","article-title":"Extension by zero in discrete trace spaces: inverse estimates","volume":"84","author":"Hiptmair, Ralf","year":"2015","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"17","doi-asserted-by":"publisher","first-page":"969","DOI":"10.1093\/imanum\/dru023","article-title":"Strong coupling of finite element methods for the Stokes-Darcy problem","volume":"35","author":"M\u00e1rquez, Antonio","year":"2015","journal-title":"IMA J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-4979","issn-type":"print"},{"issue":"3","key":"18","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/BF01396415","article-title":"Mixed finite elements in \ud835\udc45\u00b3","volume":"35","author":"N\u00e9d\u00e9lec, J.-C.","year":"1980","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"1","key":"19","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/BF01389668","article-title":"A new family of mixed finite elements in \ud835\udc45\u00b3","volume":"50","author":"N\u00e9d\u00e9lec, J.-C.","year":"1986","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"41","key":"20","first-page":"19","article-title":"Infimum-supremum","author":"Sayas, Francisco Javier","year":"2007","journal-title":"Bol. Soc. Esp. Mat. Apl. SeMA","ISSN":"https:\/\/id.crossref.org\/issn\/1575-9822","issn-type":"print"},{"issue":"262","key":"21","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1090\/S0025-5718-07-02030-3","article-title":"A posteriori error estimates for Maxwell equations","volume":"77","author":"Sch\u00f6berl, Joachim","year":"2008","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"190","key":"22","doi-asserted-by":"publisher","first-page":"483","DOI":"10.2307\/2008497","article-title":"Finite element interpolation of nonsmooth functions satisfying boundary conditions","volume":"54","author":"Scott, L. Ridgway","year":"1990","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"23","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s002110100308","article-title":"Some observations on Babu\u0161ka and Brezzi theories","volume":"94","author":"Xu, Jinchao","year":"2003","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"24","doi-asserted-by":"crossref","unstructured":"O. B. Widlund, An Extension Theorem for Finite Element Spaces with Three Applications, Proceedings of a GAMM Seminar on Numerical Techniques in Continuum Mechanics, held in Kiel, Germany, January 17-19, 1986 (Wolfgang Hackbusch and Kristian Witsch, eds.), Friedr. Vieweg and Sohn, Braunschweig\/Wiesbaden, 1987, pp. 110-122.","DOI":"10.1007\/978-3-322-85997-6_11"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2016-85-302\/S0025-5718-2016-03074-4\/S0025-5718-2016-03074-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-302\/S0025-5718-2016-03074-4\/S0025-5718-2016-03074-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:56:19Z","timestamp":1776797779000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-302\/S0025-5718-2016-03074-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,14]]},"references-count":24,"journal-issue":{"issue":"302","published-print":{"date-parts":[[2016,11]]}},"alternative-id":["S0025-5718-2016-03074-4"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3074","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":[[2016,1,14]]}}}