{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:54:25Z","timestamp":1772268865623,"version":"3.50.1"},"reference-count":29,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab.\nWe give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes.\nThroughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in\nfunctions and vectorization.\nThis paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible \u2013 an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab.\nNumerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use.\nOur implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.<\/jats:p>","DOI":"10.1515\/cmam-2018-0220","type":"journal-article","created":{"date-parts":[[2019,10,14]],"date-time":"2019-10-14T07:41:46Z","timestamp":1571038906000},"page":"459-479","source":"Crossref","is-referenced-by-count":29,"title":["Adaptive Mesh Refinement in 2D \u2013 An Efficient Implementation in Matlab"],"prefix":"10.1515","volume":"20","author":[{"given":"Stefan A.","family":"Funken","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Numerische Mathematik , Universit\u00e4t Ulm , Helmholtzstra\u00dfe 20, 89081 Ulm , Germany"}]},{"given":"Anja","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Numerische Mathematik , Universit\u00e4t Ulm , Helmholtzstra\u00dfe 20, 89081 Ulm , Germany"}]}],"member":"374","published-online":{"date-parts":[[2019,10,13]]},"reference":[{"key":"2023033110434142887_j_cmam-2018-0220_ref_001","doi-asserted-by":"crossref","unstructured":"J.  Alberty, C.  Carstensen and S. A.  Funken,\nRemarks around 50 lines of Matlab: Short finite element implementation,\nNumer. Algorithms 20 (1999), no. 2\u20133, 117\u2013137.","DOI":"10.1023\/A:1019155918070"},{"key":"2023033110434142887_j_cmam-2018-0220_ref_002","doi-asserted-by":"crossref","unstructured":"I.  Babu\u0161ka and M.  Vogelius,\nFeedback and adaptive finite element solution of one-dimensional boundary value problems,\nNumer. Math. 44 (1984), no. 1, 75\u2013102.","DOI":"10.1007\/BF01389757"},{"key":"2023033110434142887_j_cmam-2018-0220_ref_003","doi-asserted-by":"crossref","unstructured":"R. E.  Bank and A. H.  Sherman,\nAn adaptive, multilevel method for elliptic boundary value problems,\nComputing 26 (1981), no. 2, 91\u2013105.","DOI":"10.1007\/BF02241777"},{"key":"2023033110434142887_j_cmam-2018-0220_ref_004","unstructured":"R. E.  Bank, A. H.  Sherman and A.  Weiser,\nRefinement algorithms and data structures for regular local mesh refinement,\nScientific Computing (Montreal 1982),\nIMACS, New Brunswick (1983), 3\u201317."},{"key":"2023033110434142887_j_cmam-2018-0220_ref_005","doi-asserted-by":"crossref","unstructured":"P.  Binev, W.  Dahmen and R.  DeVore,\nAdaptive finite element methods with convergence rates,\nNumer. Math. 97 (2004), no. 2, 219\u2013268.","DOI":"10.1007\/s00211-003-0492-7"},{"key":"2023033110434142887_j_cmam-2018-0220_ref_006","doi-asserted-by":"crossref","unstructured":"D.  Braess,\nFinite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, 3rd ed.,\nCambridge University Press, Cambridge, 2007.","DOI":"10.1017\/CBO9780511618635"},{"key":"2023033110434142887_j_cmam-2018-0220_ref_007","doi-asserted-by":"crossref","unstructured":"C.  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