{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T08:23:02Z","timestamp":1782289382832,"version":"3.54.5"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"262","license":[{"start":{"date-parts":[[2008,12,20]],"date-time":"2008-12-20T00:00:00Z","timestamp":1229731200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, has proved to be an effective tool in finite element exterior calculus. The advantage of these operators is that they are\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    bounded projections, and still they commute with the exterior derivative. In the present paper we generalize the construction of these smoothed projections, such that also non-quasi-uniform meshes and essential boundary conditions are covered. The new tool introduced here is a space-dependent smoothing operator that commutes with the exterior derivative.\n                  <\/p>","DOI":"10.1090\/s0025-5718-07-02081-9","type":"journal-article","created":{"date-parts":[[2008,1,15]],"date-time":"2008-01-15T12:55:08Z","timestamp":1200401708000},"page":"813-829","source":"Crossref","is-referenced-by-count":82,"title":["Smoothed projections in finite element exterior calculus"],"prefix":"10.1090","volume":"77","author":[{"given":"Snorre","family":"Christiansen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ragnar","family":"Winther","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2007,12,20]]},"reference":[{"key":"1","isbn-type":"print","first-page":"137","article-title":"Differential complexes and numerical stability","author":"Arnold, Douglas N.","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/7040086905"},{"key":"2","series-title":"The IMA Volumes in Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-38034-5","volume-title":"Compatible spatial discretizations","volume":"142","year":"2006","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387309163"},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/0-387-38034-5_3","article-title":"Differential complexes and stability of finite element methods. II. The elasticity complex","author":"Arnold, Douglas N.","year":"2006","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387309163"},{"key":"4","isbn-type":"print","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492906210018","article-title":"Finite element exterior calculus, homological techniques, and applications","volume":"15","author":"Arnold, Douglas N.","year":"2006","ISBN":"https:\/\/id.crossref.org\/isbn\/0521868157","journal-title":"Acta Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0962-4929","issn-type":"print"},{"key":"5","doi-asserted-by":"crossref","unstructured":"A. Bossavit, Whitney forms: A class of finite elements for three-dimensional computations in electromagnetism, IEE Trans. Mag. 135, Part A (1988), pp. 493\u2013500.","DOI":"10.1049\/ip-a-1.1988.0077"},{"key":"6","doi-asserted-by":"crossref","unstructured":"S. H. Christiansen, Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimensions, Numer. Math. 107 (2007), pp. 87\u2013106.","DOI":"10.1007\/s00211-007-0081-2"},{"issue":"1-4","key":"7","first-page":"1","article-title":"Riemannian structures and triangulations of manifolds","volume":"40","author":"Dodziuk, J.","year":"1976","journal-title":"J. Indian Math. Soc. (N.S.)","ISSN":"https:\/\/id.crossref.org\/issn\/0019-5839","issn-type":"print"},{"issue":"228","key":"8","doi-asserted-by":"publisher","first-page":"1325","DOI":"10.1090\/S0025-5718-99-01166-7","article-title":"Canonical construction of finite elements","volume":"68","author":"Hiptmair, R.","year":"1999","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"9","doi-asserted-by":"crossref","unstructured":"R. Hiptmair, Higher order Whitney forms, in Geometrical methods in computational electromagnetics (F. Teixeira, ed.), Vol. 32 of PIER, EMW Publishing, Cambridge, MA, pp. 271\u2013299.","DOI":"10.2528\/PIER00080111"},{"key":"10","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1017\/S0962492902000041","article-title":"Finite elements in computational electromagnetism","volume":"11","author":"Hiptmair, R.","year":"2002","journal-title":"Acta Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0962-4929","issn-type":"print"},{"issue":"3","key":"11","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":"12","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"},{"key":"13","unstructured":"J. Sch\u00f6berl, A multilevel decomposition result in \ud835\udc3b(]olf), Proceedings from the 8th European Multigrid, Multilevel, and Multiscale Conference, Scheveningen, The Hague, 2005."},{"key":"14","unstructured":"J. Sch\u00f6berl, A posteriori error estimates for Maxwell equations, RICAM\u2013Report No. 2005-10. To appear in Math. Comp. (2008)"},{"key":"15","doi-asserted-by":"crossref","DOI":"10.1515\/9781400877577","volume-title":"Geometric integration theory","author":"Whitney, Hassler","year":"1957"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2008-77-262\/S0025-5718-07-02081-9\/S0025-5718-07-02081-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2008-77-262\/S0025-5718-07-02081-9\/S0025-5718-07-02081-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:18:23Z","timestamp":1776784703000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2008-77-262\/S0025-5718-07-02081-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12,20]]},"references-count":15,"journal-issue":{"issue":"262","published-print":{"date-parts":[[2008,4]]}},"alternative-id":["S0025-5718-07-02081-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-07-02081-9","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":[[2007,12,20]]}}}