{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T01:38:59Z","timestamp":1780450739420,"version":"3.54.1"},"reference-count":40,"publisher":"American Mathematical Society (AMS)","issue":"314","license":[{"start":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T00:00:00Z","timestamp":1550620800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    An interior-penalty discontinuous Galerkin (dG) method for an \\penalty-10000 elliptic interface problem involving, possibly, curved interfaces, with flux-\\penalty-10000 balancing interface conditions, e.g., modelling mass transfer of solutes through semi-permeable membranes, is considered. The method allows for\n                    <italic>extremely general curved<\/italic>\n                    element shapes employed to resolve the interface geometry exactly. A residual-type a posteriori error estimator for this dG method is proposed and upper and lower bounds of the error in the respective dG-energy norm are proven. The a posteriori error bounds are subsequently used to prove a basic a priori convergence result. The theory presented is complemented by a series of numerical experiments. The presented approach applies immediately to the case of curved domains with non-essential boundary conditions, too.\n                  <\/p>","DOI":"10.1090\/mcom\/3322","type":"journal-article","created":{"date-parts":[[2017,9,20]],"date-time":"2017-09-20T09:33:21Z","timestamp":1505900001000},"page":"2675-2707","source":"Crossref","is-referenced-by-count":41,"title":["Adaptive discontinuous Galerkin methods for elliptic interface problems"],"prefix":"10.1090","volume":"87","author":[{"given":"Andrea","family":"Cangiani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emmanuil","family":"Georgoulis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Younis","family":"Sabawi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2018,2,20]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/chel\/369","volume-title":"Lectures on elliptic boundary value problems","author":"Agmon, Shmuel","year":"2010","ISBN":"https:\/\/id.crossref.org\/isbn\/9780821849101"},{"key":"2","unstructured":"M. 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