{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T12:12:37Z","timestamp":1680264757061},"reference-count":15,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2019,1,22]],"date-time":"2019-01-22T00:00:00Z","timestamp":1548115200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003958","name":"Stichting voor de Technische Wetenschappen","doi-asserted-by":"publisher","award":["613.001.652"],"award-info":[{"award-number":["613.001.652"]}],"id":[{"id":"10.13039\/501100003958","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>For the Poisson problem in two dimensions, posed on a domain partitioned into\naxis-aligned rectangles with up to one hanging node per edge, we envision an\nefficient error reduction step in an instance-optimal <jats:italic>hp<\/jats:italic>-adaptive finite\nelement method. Central to this is the problem: Which increase in local polynomial degree\nensures <jats:italic>p<\/jats:italic>-robust contraction of the error in energy norm? We reduce this problem to a small\nnumber of saturation problems on the reference square, and provide strong numerical\nevidence for their solution.<\/jats:p>","DOI":"10.1515\/cmam-2018-0136","type":"journal-article","created":{"date-parts":[[2019,1,22]],"date-time":"2019-01-22T18:56:56Z","timestamp":1548183416000},"page":"169-186","source":"Crossref","is-referenced-by-count":0,"title":["On <i>p<\/i>-Robust Saturation on Quadrangulations"],"prefix":"10.1515","volume":"20","author":[{"given":"Jan","family":"Westerdiep","sequence":"first","affiliation":[{"name":"Korteweg-de Vries Institute for Mathematics , University of Amsterdam , P.O. Box 94248, 1090 GE Amsterdam , The Netherlands"}]}],"member":"374","published-online":{"date-parts":[[2019,1,22]]},"reference":[{"key":"2023033110163484078_j_cmam-2018-0136_ref_001","doi-asserted-by":"crossref","unstructured":"P.  Binev,\nTree Approximation for hp-Adaptivity,\nSIAM J. Numer. Anal. 56 (2018), no. 6, 3346\u20133357.","DOI":"10.1137\/18M1175070"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_002","doi-asserted-by":"crossref","unstructured":"D.  Braess, V.  Pillwein and J.  Sch\u00f6berl,\nEquilibrated residual error estimates are p-robust,\nComput. Methods Appl. Mech. Engrg. 198 (2009), no. 13\u201314, 1189\u20131197.","DOI":"10.1016\/j.cma.2008.12.010"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_003","doi-asserted-by":"crossref","unstructured":"S. C.  Brenner and L. R.  Scott,\nThe Mathematical Theory of Finite Element Methods, 3rd ed.,\nTexts Appl. Math. 15,\nSpringer, New York, 2008.","DOI":"10.1007\/978-0-387-75934-0"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_004","unstructured":"C.  Canuto, R. H.  Nochetto, R.  Stevenson and M.  Verani,\nA saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square,\nMOX-Report no. 02\/2018, Politecnico di Milano, Milano, 2017."},{"key":"2023033110163484078_j_cmam-2018-0136_ref_005","doi-asserted-by":"crossref","unstructured":"C.  Canuto, R. H.  Nochetto, R.  Stevenson and M.  Verani,\nConvergence and optimality of \n                  \n                     \n                        \ud835\udc21\ud835\udc29\n                     \n                     \n                     {\\mathbf{hp}}\n                  \n               -AFEM,\nNumer. Math. 135 (2017), no. 4, 1073\u20131119.","DOI":"10.1007\/s00211-016-0826-x"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_006","doi-asserted-by":"crossref","unstructured":"C.  Canuto, R. H.  Nochetto, R.  Stevenson and M.  Verani,\nOn p-robust saturation for hp-AFEM,\nComput. Math. Appl. 73 (2017), no. 9, 2004\u20132022.","DOI":"10.1016\/j.camwa.2017.02.035"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_007","doi-asserted-by":"crossref","unstructured":"C.  Carstensen and S. A.  Funken,\nFully reliable localized error control in the FEM,\nSIAM J. Sci. Comput. 21 (1999\/00), no. 4, 1465\u20131484.","DOI":"10.1137\/S1064827597327486"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_008","doi-asserted-by":"crossref","unstructured":"M.  Costabel, M.  Dauge and L.  Demkowicz,\nPolynomial extension operators for \n                  \n                     \n                        \n                           H\n                           1\n                        \n                     \n                     \n                     H^{1}\n                  \n               , \n                  \n                     \n                        \n                           H\n                           \u2062\n                           \n                              (\n                              curl\n                              )\n                           \n                        \n                     \n                     \n                     H(\\rm curl)\n                  \n                and \n                  \n                     \n                        \n                           H\n                           \u2062\n                           \n                              (\n                              div\n                              )\n                           \n                        \n                     \n                     \n                     H(\\rm div)\n                  \n               -spaces on a cube,\nMath. Comp. 77 (2008), no. 264, 1967\u20131999.","DOI":"10.1090\/S0025-5718-08-02108-X"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_009","doi-asserted-by":"crossref","unstructured":"V.  Dolej\u0161\u00ed, A.  Ern and M.  Vohral\u00edk,\nhp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems,\nSIAM J. Sci. Comput. 38 (2016), no. 5, A3220\u2013A3246.","DOI":"10.1137\/15M1026687"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_010","doi-asserted-by":"crossref","unstructured":"A.  Ern, I.  Smears and M.  Vohral\u00edk,\nDiscrete p-robust \n                  \n                     \n                        \n                           H\n                           \u2062\n                           \n                              (\n                              div\n                              )\n                           \n                        \n                     \n                     \n                     H({\\rm div})\n                  \n               -liftings and a posteriori estimates for elliptic problems with \n                  \n                     \n                        \n                           H\n                           \n                              -\n                              1\n                           \n                        \n                     \n                     \n                     H^{-1}\n                  \n                source terms,\nCalcolo 54 (2017), no. 3, 1009\u20131025.","DOI":"10.1007\/s10092-017-0217-4"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_011","doi-asserted-by":"crossref","unstructured":"A.  Ern and M.  Vohral\u00edk,\nPolynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed\ndiscretizations,\nSIAM J. Numer. Anal. 53 (2015), no. 2, 1058\u20131081.","DOI":"10.1137\/130950100"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_012","doi-asserted-by":"crossref","unstructured":"B.  Guo and I.  Babu\u0161ka,\nThe h-p version of the finite element method - Part 1: The basic approximation results,\nComput. Mech. 1 (1986), 21\u201341.","DOI":"10.1007\/BF00298636"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_013","doi-asserted-by":"crossref","unstructured":"B.  Guo and I.  Babu\u0161ka,\nThe h-p version of the finite element method - Part 2: General results and applications,\nComput. Mech. 1 (1986), 203\u2013220.","DOI":"10.1007\/BF00272624"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_014","doi-asserted-by":"crossref","unstructured":"R.-C.  Li,\nRayleigh quotient based optimization methods for eigenvalue problems,\nMatrix Functions and Matrix Equations,\nSer. Contemp. Appl. Math. CAM 19,\nHigher Education Press, Beijing (2015), 76\u2013108.","DOI":"10.1142\/9789814675772_0004"},{"key":"2023033110163484078_j_cmam-2018-0136_ref_015","doi-asserted-by":"crossref","unstructured":"J. M.  Melenk and B. I.  Wohlmuth,\nOn residual-based a posteriori error estimation in hp-FEM,\nAdv. Comput. Math. 15 (2001), no. 1\u20134, 311\u2013331.","DOI":"10.1023\/A:1014268310921"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/20\/1\/article-p169.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0136\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0136\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T11:40:16Z","timestamp":1680262816000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0136\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,22]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,20]]},"published-print":{"date-parts":[[2020,1,1]]}},"alternative-id":["10.1515\/cmam-2018-0136"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2018-0136","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,22]]}}}