{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T06:51:17Z","timestamp":1789195877931,"version":"build-2803163510"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to introducing our new technique for constructing the extensions, and its application to the case of polynomial extensions from $H^{1\/2}(\\partial K)$ into $H^1(K)$, for any tetrahedron K.<\/jats:p>","DOI":"10.1137\/070698786","type":"journal-article","created":{"date-parts":[[2008,9,4]],"date-time":"2008-09-04T19:18:32Z","timestamp":1220555912000},"page":"3006-3031","source":"Crossref","is-referenced-by-count":30,"title":["Polynomial Extension Operators. Part I"],"prefix":"10.1137","volume":"46","author":[{"given":"Leszek","family":"Demkowicz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jayadeep","family":"Gopalakrishnan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joachim","family":"Sch\u00f6berl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,9,4]]},"reference":[{"key":"R1","unstructured":"M. Ainsworth and L. Demkowicz,\n                      Explicit polynomial preserving trace liftings on a triangle\n                      , Math. Nachr., to appear. See also\n                      ICES Report\n                      03-47."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0728034"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1987210201991"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(94)80028-6"},{"key":"R5","unstructured":"C. Bernardi, M. Dauge, and Y. Maday,\n                      Polynomials in the sobolev world\n                      , Technical report 07-14, IRMAR, University of Rennes, 2007."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1002\/1099-1476(20010110)24:1<9::AID-MMA191>3.0.CO;2-2"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"M. Cessenat,\n                      Mathematical methods in electromagnetism. Linear theory and applications\n                      , Ser. Adv. Math. Appl. Sci. 41, World Scientific Publishing Co. Pte. Ltd., Singapore, 1996.","DOI":"10.1142\/2938"},{"key":"R8","unstructured":"M. Costabel, M. Dauge, and L. Demkowicz,\n                      Polynomial extension operators for $H^1$, $\\bfH({\\rm \\bf curl})$, and $\\bfH({\\rm div})$ spaces on a cube\n                      , Technical report, IRMAR, Rennes, 2007."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901387932"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2004.07.007"},{"key":"R11","unstructured":"L. Demkowicz, J. Gopalakrishnan, and J. Sch\u00f6berl,\n                      Polynomial extension operators. Part\n                      II, SIAM J. Numer. Anal., submitted."},{"key":"R12","unstructured":"L. Demkowicz, J. Gopalakrishnan, and J. Sch\u00f6berl,\n                      Polynomial extension operators. Part\n                      III, in preparation."},{"key":"R13","doi-asserted-by":"crossref","unstructured":"L. Demkowicz,\n                      Polynomial Exact Sequences and Projection-based Interpolation with Applications to Maxwell Equations\n                      , in Mixed Finite Elements, Compatibility Conditions and Applications, D. Boffi and L. Gastaldi, eds., Lecture Notes in Mathematics, Springer-Verlag, 2007. See also ICES Report 06-12.","DOI":"10.1007\/978-3-540-78319-0_3"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"V. Girault and P.A. Raviart,\n                      Finite Element Methods for Navier-Stokes Equations\n                      , in Springer series in Computational Mathematics 5, Springer-Verlag, New York, 1986.","DOI":"10.1007\/978-3-642-61623-5"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2003.10.001"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-06-01884-9"},{"key":"R17","unstructured":"P. Grisvard,\n                      Elliptic Problems in Nonsmooth Domains\n                      , in Monographs and Studies in Mathematics 24, Pitman Advanced Publishing Program, Marshfield, Massachusetts, 1985."},{"key":"R18","unstructured":"N. Heuer and F. Leydecker,\n                      An extension theorem for polynomials on triangles\n                      , Technical report, BICOM, Brunel University, Uxbridge, UB8 3PH, England, 2005."},{"key":"R19","unstructured":"S. Kesavan,\n                      Topics in Functional Analysis and Applications\n                      , Wiley Eastern Limited, Bombay, 1989."},{"key":"R20","unstructured":"A. Kufner,\n                      Weighted Sobolev Spaces\n                      , A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1985. Translated from the Czech."},{"key":"R21","first-page":"463","volume":"309","author":"Maday Y.","year":"1989","journal-title":"C. R. Acad. Sci. Paris. S\u00e9r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-4442","issn-type":"print"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1990-1035939-1"},{"key":"R23","unstructured":"W. McLean,\n                      Strongly Elliptic Systems and Boundary Integral Equations\n                      , Cambridge University Press, 2000."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994267552"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drl046"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070698786","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:42Z","timestamp":1787325282000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070698786"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":25,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070698786"],"URL":"https:\/\/doi.org\/10.1137\/070698786","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}