{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:38:06Z","timestamp":1762349886777,"version":"build-2065373602"},"reference-count":32,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T00:00:00Z","timestamp":1748476800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We introduce a new\n                    <jats:italic>hp<\/jats:italic>\n                    -adaptive strategy for self-adjoint elliptic boundary value problems that does\n                    <jats:italic>not<\/jats:italic>\n                    rely on using classical a posteriori error estimators. Instead, our approach is based on a generally applicable prediction strategy for the reduction of the energy error that can be expressed in terms of local modifications of the degrees of freedom in the underlying discrete approximation space. The computations related to the proposed prediction strategy involve low-dimensional linear problems that are computationally inexpensive and highly parallelizable. The mathematical building blocks for this new concept are first developed on an abstract Hilbert space level, before they are employed within the specific context of\n                    <jats:italic>hp<\/jats:italic>\n                    -type finite element discretizations. For this particular framework, we discuss an explicit construction of\n                    <jats:italic>p<\/jats:italic>\n                    -enrichments and\n                    <jats:italic>hp<\/jats:italic>\n                    -refinements by means of an appropriate constraint coefficient technique that can be employed in any dimensions. The applicability and effectiveness of the resulting\n                    <jats:italic>hp<\/jats:italic>\n                    -adaptive strategy is illustrated with some 1- and 2-dimensional numerical examples.\n                  <\/jats:p>","DOI":"10.1515\/cmam-2023-0250","type":"journal-article","created":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T16:54:24Z","timestamp":1748624064000},"page":"777-805","source":"Crossref","is-referenced-by-count":0,"title":["An\n                    <i>hp<\/i>\n                    -Adaptive Strategy Based on Locally Predicted Error Reductions"],"prefix":"10.1515","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-6041-273X","authenticated-orcid":false,"given":"Patrick","family":"Bammer","sequence":"first","affiliation":[{"name":"Fachbereich Mathematik , 630837 Paris Lodron Universit\u00e4t Salzburg , Hellbrunner Str. 14, 5020 Salzburg , Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3691-0906","authenticated-orcid":false,"given":"Andreas","family":"Schr\u00f6der","sequence":"additional","affiliation":[{"name":"Fachbereich Mathematik , 630837 Paris Lodron Universit\u00e4t Salzburg , Hellbrunner Str. 14, 5020 Salzburg , Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1232-0637","authenticated-orcid":false,"given":"Thomas P.","family":"Wihler","sequence":"additional","affiliation":[{"name":"Mathematisches Institut , Universit\u00e4t Bern , Sidlerstr. 5, CH-3012 Bern , Switzerland"}]}],"member":"374","published-online":{"date-parts":[[2025,5,29]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"M.  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Babu\u0161ka and M.  Suri,\nThe treatment of nonhomogeneous Dirichlet boundary conditions by the p-version of the finite element method,\nNumer. Math. 55 (1989), no. 1, 97\u2013121.","key":"2025110513331397521_j_cmam-2023-0250_ref_004","DOI":"10.1007\/BF01395874"},{"doi-asserted-by":"crossref","unstructured":"I.  Babu\u0161ka and M.  Suri,\nThe p and h-p versions of the finite element method, basic principles and properties,\nSIAM Rev. 36 (1994), no. 4, 578\u2013632.","key":"2025110513331397521_j_cmam-2023-0250_ref_005","DOI":"10.1137\/1036141"},{"doi-asserted-by":"crossref","unstructured":"R.  Becker and R.  Rannacher,\nAn optimal control approach to a posteriori error estimation in finite element methods,\nActa Numer. 10 (2001), 1\u2013102.","key":"2025110513331397521_j_cmam-2023-0250_ref_006","DOI":"10.1017\/S0962492901000010"},{"doi-asserted-by":"crossref","unstructured":"A.  Byfut and A.  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Vol. 1,\nChapman & Hall\/CRC Appl. Math. Nonlinear Sci.,\nChapman & Hall\/CRC, Boca Raton, 2007.","key":"2025110513331397521_j_cmam-2023-0250_ref_009"},{"doi-asserted-by":"crossref","unstructured":"P.  Di Stolfo, A.  Schr\u00f6der, N.  Zander and S.  Kollmannsberger,\nAn easy treatment of hanging nodes in hp-finite elements,\nFinite Elem. Anal. Des. 121 (2016), 101\u2013117.","key":"2025110513331397521_j_cmam-2023-0250_ref_010","DOI":"10.1016\/j.finel.2016.07.001"},{"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.","key":"2025110513331397521_j_cmam-2023-0250_ref_011","DOI":"10.1137\/15M1026687"},{"doi-asserted-by":"crossref","unstructured":"W.  D\u00f6rfler,\nA convergent adaptive algorithm for Poisson\u2019s equation,\nSIAM J. Numer. 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Schwab,\np- and hp-FEM, Theory and Applications to Solid and Fluid Mechanics,\nOxford University, Oxford, 1998.","key":"2025110513331397521_j_cmam-2023-0250_ref_027"},{"doi-asserted-by":"crossref","unstructured":"P.  \u0160ol\u00edn, K.  Segeth and I.  Dole\u017eel,\nHigher-Order Finite Element Methods,\nStud. Adv. Math.,\nChapman & Hall\/CRC, Boca Raton, 2004.","key":"2025110513331397521_j_cmam-2023-0250_ref_028","DOI":"10.1201\/9780203488041"},{"doi-asserted-by":"crossref","unstructured":"E.  S\u00fcli and P.  Houston,\nAdaptive finite element approximation of hyperbolic problems,\nError Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics,\nLect. Notes Comput. Sci. Eng. 25,\nSpringer, Berlin (2003), 269\u2013344.","key":"2025110513331397521_j_cmam-2023-0250_ref_029","DOI":"10.1007\/978-3-662-05189-4_6"},{"unstructured":"B.  Szab\u00f3 and I.  Babu\u0161ka,\nFinite Element Analysis,\nJ. Wiley & Sons, New York, 1991.","key":"2025110513331397521_j_cmam-2023-0250_ref_030"},{"unstructured":"R.  Verf\u00fcrth,\nA Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques,\nB.G. Teubner, Stuttgart, 1996.","key":"2025110513331397521_j_cmam-2023-0250_ref_031"},{"doi-asserted-by":"crossref","unstructured":"T. P.  Wihler,\nAn hp-adaptive strategy based on continuous Sobolev embeddings,\nJ. Comput. Appl. Math. 235 (2011), no. 8, 2731\u20132739.","key":"2025110513331397521_j_cmam-2023-0250_ref_032","DOI":"10.1016\/j.cam.2010.11.023"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2023-0250\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2023-0250\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:35:02Z","timestamp":1762349702000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2023-0250\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,29]]},"references-count":32,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,6,25]]},"published-print":{"date-parts":[[2025,10,1]]}},"alternative-id":["10.1515\/cmam-2023-0250"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2023-0250","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"type":"print","value":"1609-4840"},{"type":"electronic","value":"1609-9389"}],"subject":[],"published":{"date-parts":[[2025,5,29]]}}}