{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:26Z","timestamp":1747198046959,"version":"3.40.5"},"reference-count":38,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["2044-390685587","EN 1042\/4-1"],"award-info":[{"award-number":["2044-390685587","EN 1042\/4-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The unfitted discontinuous Galerkin (UDG) method allows for\nconservative dG discretizations of partial differential equations\n(PDEs) based on cut cell meshes. It is hence particularly suitable\nfor solving continuity equations on complex-shaped bulk domains.<\/jats:p>\n               <jats:p>In this paper\nbased on and extending the PhD thesis of the second author,\nwe show how the method can be transferred to PDEs on\ncurved surfaces.\nMotivated by a class of biological model problems\ncomprising continuity equations on a static bulk domain and its\nsurface, we propose a new UDG scheme for bulk-surface models.<\/jats:p>\n               <jats:p>The method\ncombines ideas of extending surface PDEs to\nhigher-dimensional bulk domains with concepts of trace finite\nelement methods.\nA particular focus is given to the necessary steps to retain\ndiscrete analogues to conservation laws of the discretized PDEs.\nA high degree\nof geometric flexibility is achieved by using a level set\nrepresentation of the geometry. We present theoretical\nresults to prove stability of the method and to investigate its\nconservation properties. Convergence is shown in an\nenergy norm and numerical results show optimal convergence order in\nbulk\/surface <jats:inline-formula id=\"j_cmam-2020-0056_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi>H<\/m:mi>\n                              <m:mn>1<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0056_eq_0223.png\"\/>\n                        <jats:tex-math>{H^{1}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>- and <jats:inline-formula id=\"j_cmam-2020-0056_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi>L<\/m:mi>\n                              <m:mn>2<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0056_eq_0230.png\"\/>\n                        <jats:tex-math>{L^{2}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-norms.<\/jats:p>","DOI":"10.1515\/cmam-2020-0056","type":"journal-article","created":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T01:35:51Z","timestamp":1622511351000},"page":"569-591","source":"Crossref","is-referenced-by-count":1,"title":["An Unfitted dG Scheme for Coupled Bulk-Surface PDEs on Complex Geometries"],"prefix":"10.1515","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6041-8228","authenticated-orcid":false,"given":"Christian","family":"Engwer","sequence":"first","affiliation":[{"name":"Applied Mathematics: Institute for Analysis and Numerics, Department of Mathematics and Computer Science , WWU M\u00fcnster , M\u00fcnster , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sebastian","family":"Westerheide","sequence":"additional","affiliation":[{"name":"Applied Mathematics: Institute for Analysis and Numerics, Department of Mathematics and Computer Science , WWU M\u00fcnster , M\u00fcnster , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2021,6,1]]},"reference":[{"key":"2023033111373317358_j_cmam-2020-0056_ref_001","doi-asserted-by":"crossref","unstructured":"P. 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Implementation and tests in DUNE,\nComputing 82 (2008), no. 2\u20133, 121\u2013138.","DOI":"10.1007\/s00607-008-0004-9"},{"key":"2023033111373317358_j_cmam-2020-0056_ref_004","doi-asserted-by":"crossref","unstructured":"P.  Bastian, M.  Blatt, A.  Dedner, C.  Engwer, R.  Kl\u00f6fkorn, M.  Ohlberger and O.  Sander,\nA generic grid interface for parallel and adaptive scientific computing. I. Abstract framework,\nComputing 82 (2008), no. 2\u20133, 103\u2013119.","DOI":"10.1007\/s00607-008-0003-x"},{"key":"2023033111373317358_j_cmam-2020-0056_ref_005","doi-asserted-by":"crossref","unstructured":"P.  Bastian and C.  Engwer,\nAn unfitted finite element method using discontinuous Galerkin,\nInternat. J. Numer. Methods Engrg. 79 (2009), no. 12, 1557\u20131576.","DOI":"10.1002\/nme.2631"},{"key":"2023033111373317358_j_cmam-2020-0056_ref_006","unstructured":"P.  Bastian, F.  Heimann and S.  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