{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T08:33:14Z","timestamp":1792225994829,"version":"4.4.0"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We study an adaptive finite element method for the p-Laplacian like PDEs using piecewise linear, continuous functions. The error is measured by means of the quasi norm of Barrett and Liu. We provide residual based error estimators without a gap between the upper and lower bound. We show linear convergence of the algorithm which is similar to the one of Morin, Nochetto, and Siebert. All results are obtained without extra marking for the oscillation.<\/jats:p>","DOI":"10.1137\/070681508","type":"journal-article","created":{"date-parts":[[2008,2,4]],"date-time":"2008-02-04T11:37:29Z","timestamp":1202125049000},"page":"614-638","source":"Crossref","is-referenced-by-count":120,"title":["Linear Convergence of an Adaptive Finite Element Method for the\n                    <i>p<\/i>\n                    -Laplacian Equation"],"prefix":"10.1137","volume":"46","author":[{"given":"Lars","family":"Diening","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Kreuzer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,2,1]]},"reference":[{"key":"R1","first-page":"523","volume":"61","author":"Barrett J. W.","year":"1993","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"R2","unstructured":"J. W. Barrett and W. B. Liu,\n                      Finite element approximation of degenerate quasilinear elliptic and parabolic problems\n                      , in Numerical Analysis 1993 (Dundee, 1993), Pitman Res. Notes Math. Ser. 303, Longman Scientific and Technical, Harlow, UK, 1994, pp. 1\u201316."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0731022"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502416617"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-06-01819-9"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1515\/FORUM.2008.027"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0733054"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-007-0079-9"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"C. Ebmeyer,\n                      \n                        Gobal regularity in Sobolev spaces for elliptic problems with\n                        p\n                        -structure on bounded domains\n                      \n                      , in Trends in Partial Differential Equations of Mathematical Physics, Progr. Nonlinear Differential Equations Appl. 61, Birkh\u00e4user, Basel, 2005, pp. 81\u201389.","DOI":"10.1007\/3-7643-7317-2_7"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-005-0594-5"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.4171\/ZAA\/1245"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"E. Giusti,\n                      Direct Methods in the Calculus of Variations\n                      , World Scientific, River Edge, NJ, 2003.","DOI":"10.1142\/5002"},{"key":"R13","first-page":"41","volume":"9","author":"Glowinski R.","year":"1975","journal-title":"Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationelle Ser. 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