{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T20:45:43Z","timestamp":1754599543990,"version":"3.38.0"},"reference-count":35,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T00:00:00Z","timestamp":1728259200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"NSF DMS","award":["2309606"],"award-info":[{"award-number":["2309606"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Inspired by the methods developed in J. H. Bramble, T. Dupont, and V. Thom\u00e9e (\u201cProjection methods for Dirichlet\u2019s problem in approximating polygonal domains with boundary-value corrections,\u201d <jats:italic>Math. Comput.<\/jats:italic>, vol. 26, no. 120, pp. 869\u2013879, 1972), we introduce a new technique that yields a symmetric formulation and has similar performance. The new method is based on a Robin-type problem on an approximate polygonal domain. Optimal error estimates in the energy norm\u202fare proved for piecewise quadratics and cubics. We provide numerical experiments that show our theoretical results are sharp.<\/jats:p>","DOI":"10.1515\/jnma-2023-0135","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T12:21:45Z","timestamp":1728044505000},"page":"55-86","source":"Crossref","is-referenced-by-count":1,"title":["Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated"],"prefix":"10.1515","volume":"33","author":[{"given":"Todd","family":"Dupont","sequence":"first","affiliation":[{"name":"Departments of Computer Science and of Mathematics , The University of Chicago , Chicago , IL 60637 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6769-2393","authenticated-orcid":false,"given":"Johnny","family":"Guzm\u00e1n","sequence":"additional","affiliation":[{"name":"Division of Applied Mathematics , Brown University , Box F, 182 George Street , Providence , RI 02912 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7885-7106","authenticated-orcid":false,"given":"L. Ridgway","family":"Scott","sequence":"additional","affiliation":[{"name":"The University of Chicago, Emeritus , Chicago , IL 60637 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,10,7]]},"reference":[{"key":"2025022817485525524_j_jnma-2023-0135_ref_001","unstructured":"A. Berger, R. Scott, and G. Strang, \u201cApproximate boundary conditions in the finite element method,\u201d in Symposia Mathematica, vol. 10, London, Academic Press, 1972, pp. 295\u2013313."},{"key":"2025022817485525524_j_jnma-2023-0135_ref_002","doi-asserted-by":"crossref","unstructured":"Z. Li, T. Lin, and X. Wu, \u201cNew cartesian grid methods for interface problems using the finite element formulation,\u201d Numer. Math., vol.\u00a096, no.\u00a01, pp.\u00a061\u201398, 2003. https:\/\/doi.org\/10.1007\/s00211-003-0473-x.","DOI":"10.1007\/s00211-003-0473-x"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_003","unstructured":"L. R. Scott, \u201cFinite element techniques for curved boundaries,\u201d Ph.D. dissertation, Massachusetts Institute of Technology, 1973."},{"key":"2025022817485525524_j_jnma-2023-0135_ref_004","doi-asserted-by":"crossref","unstructured":"R. Scott, \u201cInterpolated boundary conditions in the finite element method,\u201d SIAM J. Numer. Anal., vol.\u00a012, no.\u00a03, pp.\u00a0404\u2013427, 1975. https:\/\/doi.org\/10.1137\/0712032.","DOI":"10.1137\/0712032"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_005","doi-asserted-by":"crossref","unstructured":"J. Nitsche, \u201c\u00dcber ein Variationsprinzip zur L\u00f6sung von Dirichlet-Problemen bei Verwendung von Teilr\u00e4umen, die keinen Randbedingungen unterworfen sind,\u201d Abh. Math. Semin. Univ. Hambg., vol.\u00a036, no.\u00a01, pp.\u00a09\u201315, 1971. https:\/\/doi.org\/10.1007\/bf02995904.","DOI":"10.1007\/BF02995904"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_006","doi-asserted-by":"crossref","unstructured":"A. Hansbo and P. Hansbo, \u201cAn unfitted finite element method, based on Nitsche\u2019s method, for elliptic interface problems,\u201d Comput. Methods Appl. Mech. Eng., vol.\u00a0191, nos. 47\u201348, pp.\u00a05537\u20135552, 2002. https:\/\/doi.org\/10.1016\/s0045-7825(02)00524-8.","DOI":"10.1016\/S0045-7825(02)00524-8"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_007","doi-asserted-by":"crossref","unstructured":"E. Burman, \u201cGhost penalty,\u201d C. R. Math., vol.\u00a0348, nos. 21\u201322, pp.\u00a01217\u20131220, 2010. https:\/\/doi.org\/10.1016\/j.crma.2010.10.006.","DOI":"10.1016\/j.crma.2010.10.006"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_008","doi-asserted-by":"crossref","unstructured":"J. H. Bramble, T. Dupont, and V. Thom\u00e9e, \u201cProjection methods for Dirichlet\u2019s problem in approximating polygonal domains with boundary-value corrections,\u201d Math. Comput., vol.\u00a026, no.\u00a0120, pp.\u00a0869\u2013879, 1972. https:\/\/doi.org\/10.1090\/s0025-5718-1972-0343657-7.","DOI":"10.1090\/S0025-5718-1972-0343657-7"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_009","doi-asserted-by":"crossref","unstructured":"J. H. Bramble and J. T. King, \u201cA robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries,\u201d Math. Comput., vol.\u00a063, no.\u00a0207, pp.\u00a01\u201317, 1994. https:\/\/doi.org\/10.2307\/2153559.","DOI":"10.1090\/S0025-5718-1994-1242055-6"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_010","doi-asserted-by":"crossref","unstructured":"E. Burman, P. Hansbo, and M. Larson, \u201cA cut finite element method with boundary value correction,\u201d Math. Comput., vol.\u00a087, no.\u00a0310, pp.\u00a0633\u2013657, 2018. https:\/\/doi.org\/10.1090\/mcom\/3240.","DOI":"10.1090\/mcom\/3240"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_011","doi-asserted-by":"crossref","unstructured":"E. Burman, P. Hansbo, and M. G. Larson, \u201cDirichlet boundary value correction using Lagrange multipliers,\u201d BIT Numer. Math., vol.\u00a060, no.\u00a01, pp.\u00a0235\u2013260, 2020. https:\/\/doi.org\/10.1007\/s10543-019-00773-4.","DOI":"10.1007\/s10543-019-00773-4"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_012","doi-asserted-by":"crossref","unstructured":"J. Cheung, M. Perego, P. Bochev, and M. Gunzburger, \u201cOptimally accurate higher-order finite element methods for polytopial approximations of domains with smooth boundaries,\u201d Math. Comput., vol.\u00a088, no.\u00a0319, pp.\u00a02187\u20132219, 2019. https:\/\/doi.org\/10.1090\/mcom\/3415.","DOI":"10.1090\/mcom\/3415"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_013","doi-asserted-by":"crossref","unstructured":"B. Cockburn, W. Qiu, and M. Solano, \u201cA priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity,\u201d Math. Comput., vol.\u00a083, no.\u00a0286, pp.\u00a0665\u2013699, 2014. https:\/\/doi.org\/10.1090\/s0025-5718-2013-02747-0.","DOI":"10.1090\/S0025-5718-2013-02747-0"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_014","doi-asserted-by":"crossref","unstructured":"B. Cockburn and M. Solano, \u201cSolving dirichlet boundary-value problems on curved domains by extensions from subdomains,\u201d SIAM J. Sci. 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Scovazzi, \u201cThe shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems,\u201d J. Comput. Phys., vol.\u00a0372, pp.\u00a0972\u2013995, 2018, https:\/\/doi.org\/10.1016\/j.jcp.2017.10.026.","DOI":"10.1016\/j.jcp.2017.10.026"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_018","doi-asserted-by":"crossref","unstructured":"A. Main and G. Scovazzi, \u201cThe shifted boundary method for embedded domain computations. Part II: linear advection\u2013diffusion and incompressible Navier\u2013Stokes equations,\u201d J. Comput. Phys., vol.\u00a0372, pp.\u00a0996\u20131026, 2018, https:\/\/doi.org\/10.1016\/j.jcp.2018.01.023.","DOI":"10.1016\/j.jcp.2018.01.023"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_019","doi-asserted-by":"crossref","unstructured":"M. Solano and F. Vargas, \u201cA high order HDG method for Stokes flow in curved domains,\u201d J. Sci. 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Oyarz\u00faa, M. Solano, and P. Z\u00fa\u00f1iga, \u201cA high order mixed-fem for diffusion problems on curved domains,\u201d J. Sci. Comput., vol.\u00a079, no.\u00a01, pp.\u00a049\u201378, 2019. https:\/\/doi.org\/10.1007\/s10915-018-0840-5.","DOI":"10.1007\/s10915-018-0840-5"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_029","doi-asserted-by":"crossref","unstructured":"R. Oyarz\u00faa, M. Solano, and P. Z\u00fa\u00f1iga, \u201cA priori and a posteriori error analyses of a high order unfitted mixed-FEM for Stokes flow,\u201d Comput. Methods Appl. Mech. Eng., vol.\u00a0360, p.\u00a0112780, 2020, https:\/\/doi.org\/10.1016\/j.cma.2019.112780.","DOI":"10.1016\/j.cma.2019.112780"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_030","doi-asserted-by":"crossref","unstructured":"L. Blank, A. Caiazzo, F. Chouly, A. Lozinski, and J. Mura, \u201cAnalysis of a stabilized penalty-free Nitsche method for the Brinkman, Stokes, and Darcy problems,\u201d ESAIM: Math. Model. Numer. Anal., vol.\u00a052, no.\u00a06, pp.\u00a02149\u20132185, 2018. https:\/\/doi.org\/10.1051\/m2an\/2018063.","DOI":"10.1051\/m2an\/2018063"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_031","doi-asserted-by":"crossref","unstructured":"T. Boiveau, E. Burman, and S. Claus, \u201cPenalty-free Nitsche method for interface problems,\u201d in Geometrically Unfitted Finite Element Methods and Applications, New York, Springer, 2017, pp. 183\u2013210.","DOI":"10.1007\/978-3-319-71431-8_6"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_032","doi-asserted-by":"crossref","unstructured":"E. Burman, \u201cA penalty-free nonsymmetric Nitsche-type method for the weak imposition of boundary conditions,\u201d SIAM J. Numer. Anal., vol.\u00a050, no.\u00a04, pp.\u00a01959\u20131981, 2012. https:\/\/doi.org\/10.1137\/10081784x.","DOI":"10.1137\/10081784X"},{"key":"2025022817485525524_j_jnma-2023-0135_ref_033","doi-asserted-by":"crossref","unstructured":"A. Logg, K. A. Mardal, and G. Wells, Eds. 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Tscherpel, \u201cHigh-order Stokes approximation on polygonally approximated curved boundaries,\u201d in preparation, 2024."}],"container-title":["Journal of Numerical Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jnma-2023-0135\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jnma-2023-0135\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T17:49:18Z","timestamp":1740764958000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jnma-2023-0135\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,7]]},"references-count":35,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,3,30]]},"published-print":{"date-parts":[[2025,3,26]]}},"alternative-id":["10.1515\/jnma-2023-0135"],"URL":"https:\/\/doi.org\/10.1515\/jnma-2023-0135","relation":{},"ISSN":["1570-2820","1569-3953"],"issn-type":[{"type":"print","value":"1570-2820"},{"type":"electronic","value":"1569-3953"}],"subject":[],"published":{"date-parts":[[2024,10,7]]}}}