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The dual (i.e., adjoint)\nsolution is obtained via\na local higher-order approximation using a single element.\nOur algorithmic developments are substantiated\nwith the help of several numerical tests.<\/jats:p>","DOI":"10.1515\/cmam-2017-0046","type":"journal-article","created":{"date-parts":[[2017,11,12]],"date-time":"2017-11-12T22:16:29Z","timestamp":1510524989000},"page":"753-776","source":"Crossref","is-referenced-by-count":16,"title":["The Dual-Weighted Residual Estimator Realized on Polygonal Meshes"],"prefix":"10.1515","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8507-9413","authenticated-orcid":false,"given":"Steffen","family":"Wei\u00dfer","sequence":"first","affiliation":[{"name":"Applied Mathematics , Saarland University , Campus, 66041 Saarbr\u00fccken , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Wick","sequence":"additional","affiliation":[{"name":"Centre de Math\u00e9matiques Appliqu\u00e9es , \u00c9cole Polytechnique , Universit\u00e9 Paris-Saclay , 91128 Palaiseau , France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,11,12]]},"reference":[{"key":"2023033110390200992_j_cmam-2017-0046_ref_001_w2aab3b7e1444b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"M.  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Wei\u00dfer,\nFinite Element Methods with local Trefftz trial functions,\nPh.D. thesis, Universit\u00e4t des Saarlandes, Saarbr\u00fccken, 2012."},{"key":"2023033110390200992_j_cmam-2017-0046_ref_044_w2aab3b7e1444b1b6b1ab2ac44Aa","doi-asserted-by":"crossref","unstructured":"S.  Wei\u00dfer,\nArbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM,\nComput. Math. Appl. 67 (2014), no. 7, 1390\u20131406.","DOI":"10.1016\/j.camwa.2014.01.019"},{"key":"2023033110390200992_j_cmam-2017-0046_ref_045_w2aab3b7e1444b1b6b1ab2ac45Aa","doi-asserted-by":"crossref","unstructured":"S.  Wei\u00dfer,\nResidual based error estimate for higher order Trefftz-like trial functions on adaptively refined polygonal meshes,\nNumerical Mathematics and Advanced Applications\u2014ENUMATH 2013,\nLect. Notes Comput. Sci. Eng. 103,\nSpringer, Cham (2015), 233\u2013241.","DOI":"10.1007\/978-3-319-10705-9_23"},{"key":"2023033110390200992_j_cmam-2017-0046_ref_046_w2aab3b7e1444b1b6b1ab2ac46Aa","doi-asserted-by":"crossref","unstructured":"S.  Wei\u00dfer,\nResidual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM,\nComput. Math. Appl. 73 (2017), no. 2, 187\u2013202.","DOI":"10.1016\/j.camwa.2016.11.013"},{"key":"2023033110390200992_j_cmam-2017-0046_ref_047_w2aab3b7e1444b1b6b1ab2ac47Aa","doi-asserted-by":"crossref","unstructured":"T.  Wick,\nGoal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity,\nComput. Mech. 57 (2016), no. 6, 1017\u20131035.","DOI":"10.1007\/s00466-016-1275-1"},{"key":"2023033110390200992_j_cmam-2017-0046_ref_048_w2aab3b7e1444b1b6b1ab2ac48Aa","doi-asserted-by":"crossref","unstructured":"K.  Zee, E.  Brummelen, I.  Akkerman and R.  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