{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:37:56Z","timestamp":1762349876328,"version":"build-2065373602"},"reference-count":24,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-22-08404"],"award-info":[{"award-number":["DMS-22-08404"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We develop a finite element method for an elliptic Maxwell boundary value problem\non polyhedral domains in\n                    <jats:inline-formula id=\"j_cmam-2025-0100_ineq_9999\">\n                      <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <m:msup>\n                            <m:mi>\u211d<\/m:mi>\n                            <m:mn>3<\/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-2025-0100_eq_0542.png\"\/>\n                        <jats:tex-math>{\\mathbb{R}^{3}}<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    with a general topology. Our method is based on a\nHodge decomposition approach that leads to standard scalar elliptic problems and elliptic saddle point problems for vector\npotentials that have previously been\ninvestigated in the study of fluid flow problems. We carry out an error analysis that does not involve\nassumed regularity of the solution and present corroborating numerical results.\n                  <\/jats:p>","DOI":"10.1515\/cmam-2025-0100","type":"journal-article","created":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T06:39:32Z","timestamp":1756449572000},"page":"823-848","source":"Crossref","is-referenced-by-count":0,"title":["A Hodge Decomposition Finite Element Method for an Elliptic Maxwell Boundary Value Problem on General Polyhedral Domains"],"prefix":"10.1515","volume":"25","author":[{"given":"Susanne C.","family":"Brenner","sequence":"first","affiliation":[{"name":"Department of Mathematics and Center for Computation & Technology , 124525 Louisiana State University , Baton Rouge , LA 70803 , USA"}]},{"given":"Casey","family":"Cavanaugh","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Center for Computation & Technology , 124525 Louisiana State University , Baton Rouge , LA 70803 , USA"}]},{"given":"Li-Yeng","family":"Sung","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Center for Computation & Technology , 124525 Louisiana State University , Baton Rouge , LA 70803 , USA"}]}],"member":"374","published-online":{"date-parts":[[2025,8,29]]},"reference":[{"key":"2025110513331291177_j_cmam-2025-0100_ref_001","unstructured":"R. A.  Adams and J. J. F.  Fournier,\nSobolev Spaces, 2nd ed.,\nPure Appl. Math. (Amsterdam) 140,\nAcademic Press, Amsterdam, 2003."},{"key":"2025110513331291177_j_cmam-2025-0100_ref_002","doi-asserted-by":"crossref","unstructured":"A.  Alonso and A.  Valli,\nAn optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations,\nMath. Comp. 68 (1999), no. 226, 607\u2013631.","DOI":"10.1090\/S0025-5718-99-01013-3"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_003","doi-asserted-by":"crossref","unstructured":"C.  Amrouche, C.  Bernardi, M.  Dauge and V.  Girault,\nVector potentials in three-dimensional non-smooth domains,\nMath. Methods Appl. Sci. 21 (1998), no. 9, 823\u2013864.","DOI":"10.1002\/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_004","doi-asserted-by":"crossref","unstructured":"F.  Assous, P.  Ciarlet and S.  Labrunie,\nMathematical Foundations of Computational Electromagnetism,\nAppl. Math. Sci. 198,\nSpringer, Cham, 2018.","DOI":"10.1007\/978-3-319-70842-3"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_005","doi-asserted-by":"crossref","unstructured":"C.  Bernardi, V.  Girault, F.  Hecht, P.-A.  Raviart and B.  Rivi\u00e8re,\nMathematics and Finite Element Discretizations of Incompressible Navier\u2013Stokes Flows,\nClass. Appl. Math. 90,\nSociety for Industrial and Applied Mathematics, Philadelphia, 2025.","DOI":"10.1137\/1.9781611978124"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_006","doi-asserted-by":"crossref","unstructured":"S. C.  Brenner, C.  Cavanaugh and L.-Y.  Sung,\nA Hodge decomposition finite element method for the quad-curl problem on polyhedral domains,\nJ. Sci. Comput. 100 (2024), no. 3, Paper No. 80.","DOI":"10.1007\/s10915-024-02626-x"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_007","doi-asserted-by":"crossref","unstructured":"S. C.  Brenner, J.  Cui, Z.  Nan and L.-Y.  Sung,\nHodge decomposition for divergence-free vector fields and two-dimensional Maxwell\u2019s equations,\nMath. Comp. 81 (2012), no. 278, 643\u2013659.","DOI":"10.1090\/S0025-5718-2011-02540-8"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_008","doi-asserted-by":"crossref","unstructured":"S. C.  Brenner, J.  Gedicke and L.-Y.  Sung,\nHodge decomposition for two-dimensional time-harmonic Maxwell\u2019s equation: Impedance boundary condition,\nMath. Methods Appl. Sci. 40 (2017), no. 2, 370\u2013390.","DOI":"10.1002\/mma.3398"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_009","doi-asserted-by":"crossref","unstructured":"S. C.  Brenner and L. R.  Scott,\nThe Mathematical Theory of Finite Element Methods, 3rd ed.,\nTexts Appl. Math. 15,\nSpringer, New York, 2008.","DOI":"10.1007\/978-0-387-75934-0"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_010","doi-asserted-by":"crossref","unstructured":"H.  Brezis,\nFunctional Analysis, Sobolev Spaces and Partial Differential Equations,\nUniversitext,\nSpringer, New York, 2011.","DOI":"10.1007\/978-0-387-70914-7"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_011","doi-asserted-by":"crossref","unstructured":"P. G.  Ciarlet,\nThe Finite Element Method for Elliptic Problems,\nStud. Math. Appl. 4,\nNorth-Holland, Amsterdam, 1978.","DOI":"10.1115\/1.3424474"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_012","doi-asserted-by":"crossref","unstructured":"M.  Dauge,\nElliptic Boundary Value Problems on Corner Domains,\nLecture Notes in Math. 1341,\nSpringer, Berlin, 1988.","DOI":"10.1007\/BFb0086682"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_013","doi-asserted-by":"crossref","unstructured":"A.  Ern and J.-L.  Guermond,\nSpectral correctness of the simplicial discontinuous Galerkin approximation of the first-order form of Maxwell\u2019s equations with discontinuous coefficients,\nSIAM J. Numer. Anal. 63 (2025), no. 2, 661\u2013684.","DOI":"10.1137\/24M1638331"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_014","doi-asserted-by":"crossref","unstructured":"V.  Girault and P.-A.  Raviart,\nFinite Element Methods for Navier\u2013Stokes Equations,\nSpringer Ser. Comput. Math. 5,\nSpringer, Berlin, 1986.","DOI":"10.1007\/978-3-642-61623-5"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_015","doi-asserted-by":"crossref","unstructured":"A.  Greenbaum,\nIterative Methods for Solving Linear Systems,\nFront. Appl. Math. 17,\nSociety for Industrial and Applied Mathematics, Philadelphia, 1997.","DOI":"10.1137\/1.9781611970937"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_016","unstructured":"P.  Grisvard,\nSingularities in Boundary Value Problems,\nRech. Math. Appl. 22,\nMasson, Paris, 1992."},{"key":"2025110513331291177_j_cmam-2025-0100_ref_017","unstructured":"J.  Jin,\nThe Finite Element Method in Electromagnetics, 2nd ed.,\nJohn Wiley & Sons, New York, 2002."},{"key":"2025110513331291177_j_cmam-2025-0100_ref_018","doi-asserted-by":"crossref","unstructured":"F.  Kikuchi,\nMixed formulations for finite element analysis of magnetostatic and electrostatic problems,\nJapan J. Appl. Math. 6 (1989), no. 2, 209\u2013221.","DOI":"10.1007\/BF03167879"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_019","doi-asserted-by":"crossref","unstructured":"V.  Maz\u2019ya and J.  Rossmann,\nElliptic Equations in Polyhedral Domains,\nMath. Surveys Monogr. 162,\nAmerican Mathematical Society, Providence 2010.","DOI":"10.1090\/surv\/162"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_020","doi-asserted-by":"crossref","unstructured":"P.  Monk,\nFinite Element Methods for Maxwell\u2019s Equations,\nNumer. Math. Sci. Comput.,\nOxford University, New York, 2003.","DOI":"10.1093\/acprof:oso\/9780198508885.001.0001"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_021","doi-asserted-by":"crossref","unstructured":"J.-C.  N\u00e9d\u00e9lec,\nMixed finite elements in \n                  \n                     \n                        \n                           \ud835\udc11\n                           3\n                        \n                     \n                     \n                     {\\mathbf{R}}^{3}\n                  \n               ,\nNumer. Math. 35 (1980), no. 3, 315\u2013341.","DOI":"10.1007\/BF01396415"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_022","doi-asserted-by":"crossref","unstructured":"J.  Peetre,\nEspaces d\u2019interpolation et th\u00e9or\u00e8me de Soboleff,\nAnn. Inst. Fourier (Grenoble) 16 (1966), 279\u2013317.","DOI":"10.5802\/aif.232"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_023","doi-asserted-by":"crossref","unstructured":"Y.  Saad,\nIterative Methods for Sparse Linear Systems,\nSociety for Industrial and Applied Mathematics, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718003"},{"key":"2025110513331291177_j_cmam-2025-0100_ref_024","doi-asserted-by":"crossref","unstructured":"A. H.  Schatz,\nAn observation concerning Ritz\u2013Galerkin methods with indefinite bilinear forms,\nMath. Comp. 28 (1974), 959\u2013962.","DOI":"10.1090\/S0025-5718-1974-0373326-0"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2025-0100\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2025-0100\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:34:48Z","timestamp":1762349688000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2025-0100\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,29]]},"references-count":24,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,6,25]]},"published-print":{"date-parts":[[2025,10,1]]}},"alternative-id":["10.1515\/cmam-2025-0100"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2025-0100","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"type":"print","value":"1609-4840"},{"type":"electronic","value":"1609-9389"}],"subject":[],"published":{"date-parts":[[2025,8,29]]}}}