{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:52:02Z","timestamp":1776847922754,"version":"3.51.2"},"reference-count":27,"publisher":"American Mathematical Society (AMS)","issue":"315","license":[{"start":{"date-parts":[[2019,4,10]],"date-time":"2019-04-10T00:00:00Z","timestamp":1554854400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100004963","name":"Seventh Framework Programme","doi-asserted-by":"publisher","award":["278011"],"award-info":[{"award-number":["278011"]}],"id":[{"id":"10.13039\/501100004963","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We develop finite element exterior calculus over weakly Lipschitz domains. Specifically, we construct commuting projections from\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L Superscript p\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    de\u00a0Rham complexes over weakly Lipschitz domains onto finite element de\u00a0Rham complexes. The projections satisfy uniform bounds for finite element spaces with bounded polynomial degree over shape-regular families of triangulations. Thus we extend the theory of finite element differential forms to polyhedral domains that are weakly Lipschitz but not strongly Lipschitz. As new mathematical tools, we use the collar theorem in the Lipschitz category, and we show that the degrees of freedom in finite element exterior calculus are flat chains in the sense of geometric measure theory.\n                  <\/p>","DOI":"10.1090\/mcom\/3329","type":"journal-article","created":{"date-parts":[[2017,10,18]],"date-time":"2017-10-18T09:30:33Z","timestamp":1508319033000},"page":"179-210","source":"Crossref","is-referenced-by-count":10,"title":["Smoothed projections over weakly Lipschitz domains"],"prefix":"10.1090","volume":"88","author":[{"given":"Martin","family":"Licht","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2018,4,10]]},"reference":[{"key":"1","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"},{"issue":"21-26","key":"2","doi-asserted-by":"publisher","first-page":"1660","DOI":"10.1016\/j.cma.2008.12.017","article-title":"Geometric decompositions and local bases for spaces of finite element differential forms","volume":"198","author":"Arnold, Douglas N.","year":"2009","journal-title":"Comput. 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