{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:26:26Z","timestamp":1787329586635,"version":"build-2736575974"},"reference-count":60,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["WO1425\/5-1"],"award-info":[{"award-number":["WO1425\/5-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["DFG EXC 1003"],"award-info":[{"award-number":["DFG EXC 1003"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["641652"],"award-info":[{"award-number":["641652"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>In order to perform electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to be simulated, which is the so-called EEG forward problem. To solve it accurately, it is necessary to apply numerical methods that are able to take the individual geometry and conductivity distribution of the subject's head into account. In this context, the finite element (FE) method (FEM) has shown high numerical accuracy with the possibility to model complex geometries and conductive features, e.g., white matter conductivity anisotropy. In this article, we introduce and analyze the application of a discontinuous Galerkin (DG) method, an FEM that includes features of the finite volume framework, to the EEG forward problem. The DG-FEM approach fulfills the conservation property of electric charge also in the discrete case, making it attractive for a variety of applications. Furthermore, as we show, this approach can alleviate modeling inaccuracies that might occur in head geometries when using classical FE methods, e.g., so-called \u201cskull leakage effects,\u201d which may occur in areas where the thickness of the skull is in the range of the mesh resolution. Therefore, we derive a DG formulation of the FEM subtraction approach for the EEG forward problem and present numerical results that highlight the advantageous features and the potential benefits of the proposed approach. (An erratum is attached.)<\/jats:p>","DOI":"10.1137\/15m1048392","type":"journal-article","created":{"date-parts":[[2017,2,23]],"date-time":"2017-02-23T14:33:26Z","timestamp":1487860406000},"page":"B138-B164","source":"Crossref","is-referenced-by-count":57,"title":["A Discontinuous Galerkin Method to Solve the EEG Forward Problem Using the Subtraction Approach"],"prefix":"10.1137","volume":"39","author":[{"given":"Christian","family":"Engwer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johannes","family":"Vorwerk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jakob","family":"Ludewig","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carsten H.","family":"Wolters","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,2,23]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jneumeth.2010.04.031"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-010-9390-1"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901384162"},{"key":"atypb4","unstructured":"\u00dc. Aydin,\n                      Combined EEG and MEG Source Analysis of Epileptiform Activity Using Calibrated Realistic Finite Element Head Models\n                      , PhD thesis, Fakult\u00e4t f\u00fcr Informatik und Automatisierung, Technische Universit\u00e4t Ilmenau, Germany, 2015,https:\/\/www.sci.utah.edu\/ wolters\/PaperWolters\/2015\/Umit_Aydin_Dissertation_2015.pdf."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0118753"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0093154"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-008-0004-9"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-008-0003-x"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1816"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2631"},{"key":"atypb12","first-page":"294","volume":"46","author":"Bastian P.","year":"2010","journal-title":"Kybernetika (Prague)"},{"key":"atypb13","first-page":"154","volume-title":"Biomagnetic Localization and 3D Modelling","author":"Bertrand O.","year":"1991"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.nicl.2014.06.005"},{"key":"atypb15","first-page":"74","volume":"1","author":"Blasche M.","year":"2012","journal-title":"Magnetom Flash"},{"key":"atypb16","volume-title":"Fast Solvers, and Applications in Solid Mechanics","author":"Braess D.","year":"2007"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511979958"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/S0013-4694(96)95698-9"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2006.09.034"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1109\/IEMBS.2006.260314"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1109\/10.245635"},{"key":"atypb22","volume-title":"Math. 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Sch\u00f6nen, A. Rien\u00e4cker, R. Beckmann, and G. Knoll,\n                      Dipolabbildung im FEM-Netz, Teil I\n                      , Arbeitspapier zum Projekt Anatomische Abbildung elektrischer Aktivit\u00e4t des Zentralnervensystems, RWTH Aachen, University\/Aachen 1994."},{"key":"atypb44","volume-title":"International Conference on Basic and Clinical Multimodal Imaging (BaCI)","author":"Sonntag H.","year":"2013"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/57\/11\/3517"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/50\/13\/004"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1007\/BF00282253"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1137\/09075038X"},{"key":"atypb49","first-page":"382","volume":"45","author":"Vatta F.","year":"2009","journal-title":"Biomed Sci Instrum"},{"key":"atypb50","unstructured":"J. Vorwerk,\n                      New finite element methods to solve the EEG\/MEG forward problem\n                      , PhD thesis, Mathematisch-Naturwissenschaftliche Fakult\u00e4t, Westf\u00e4lische-Wilhelms Universit\u00e4t M\u00fcnster, Germany, 2016,https:\/\/www.sci.utah.edu\/ wolters\/PaperWolters\/2016\/Vorwerk_Dissertation_2016.pdf."},{"key":"atypb51","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2014.06.040"},{"key":"atypb52","doi-asserted-by":"publisher","DOI":"10.1515\/bmt-2012-4152"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1088\/1741-2560\/11\/1\/016002"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1114\/1.1310220"},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2007.912427"},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1137\/0715010"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1002\/hbm.21479"},{"key":"atypb58","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/20\/4\/007"},{"key":"atypb59","doi-asserted-by":"publisher","DOI":"10.1016\/j.ics.2007.02.014"},{"key":"atypb60","doi-asserted-by":"publisher","DOI":"10.1137\/060659053"},{"key":"atypb61","doi-asserted-by":"publisher","DOI":"10.1007\/BF02442317"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/15M1048392","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:23:28Z","timestamp":1787325808000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/15M1048392"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":60,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/15M1048392"],"URL":"https:\/\/doi.org\/10.1137\/15m1048392","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}