{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T11:16:09Z","timestamp":1778584569791,"version":"3.51.4"},"reference-count":41,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100016360","name":"Zhongyuan University of Technology","doi-asserted-by":"publisher","award":["34110876"],"award-info":[{"award-number":["34110876"]}],"id":[{"id":"10.13039\/501100016360","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171244"],"award-info":[{"award-number":["12171244"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12526517"],"award-info":[{"award-number":["12526517"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006407","name":"Natural Science Foundation of Henan Province","doi-asserted-by":"publisher","award":["242300421698"],"award-info":[{"award-number":["242300421698"]}],"id":[{"id":"10.13039\/501100006407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.cnsns.2026.109902","type":"journal-article","created":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T23:51:59Z","timestamp":1773273119000},"page":"109902","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Weak Galerkin method with boundary value correction"],"prefix":"10.1016","volume":"159","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7184-234X","authenticated-orcid":false,"given":"Yi","family":"Liu","sequence":"first","affiliation":[]},{"given":"Yongli","family":"Hou","sequence":"additional","affiliation":[]},{"given":"Yanqiu","family":"Wang","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.cnsns.2026.109902_bib0001","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1137\/0124029","article-title":"Bounds for the change in the solutions of second order elliptic PDE\u2019s when the boundary is perturbed","volume":"24","author":"Blair","year":"1973","journal-title":"SIAM J Appl Math"},{"key":"10.1016\/j.cnsns.2026.109902_bib0002","series-title":"Partial differential equations","first-page":"199","article-title":"The change in solution due to change in domain","author":"Strang","year":"1973"},{"issue":"1","key":"10.1016\/j.cnsns.2026.109902_bib0003","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1093\/imamat\/11.1.33","article-title":"Polygonal domain approximation in dirichlet\u2019s problem","volume":"11","author":"Thom\u00e9e","year":"1973","journal-title":"IMA J Appl Math"},{"issue":"1","key":"10.1016\/j.cnsns.2026.109902_bib0004","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0020-7683(68)90031-0","article-title":"Curved, isoparametric,\u201cquadrilateral\u201d elements for finite element analysis","volume":"4","author":"Ergatoudis","year":"1968","journal-title":"Int J Solids Struct"},{"issue":"3","key":"10.1016\/j.cnsns.2026.109902_bib0005","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1137\/0723036","article-title":"Optimal isoparametric finite elements and error estimates for domains involving curved boundaries","volume":"23","author":"Lenoir","year":"1986","journal-title":"SIAM J Numer Anal"},{"key":"10.1016\/j.cnsns.2026.109902_bib0006","series-title":"Isogeometric analysis: toward integration of CAD and FEA","author":"Cottrell","year":"2009"},{"key":"10.1016\/j.cnsns.2026.109902_bib0007","doi-asserted-by":"crossref","first-page":"4135","DOI":"10.1016\/j.cma.2004.10.008","article-title":"Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement","volume":"194","author":"Hughes","year":"2005","journal-title":"Comput Methods Appl Mech Eng"},{"key":"10.1016\/j.cnsns.2026.109902_bib0008","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.cam.2012.10.003","article-title":"A weak Galerkin finite element method for second-order elliptic problems","volume":"241","author":"Wang","year":"2013","journal-title":"J Comput Appl Math"},{"issue":"289","key":"10.1016\/j.cnsns.2026.109902_bib0009","doi-asserted-by":"crossref","first-page":"2101","DOI":"10.1090\/S0025-5718-2014-02852-4","article-title":"A weak Galerkin mixed finite element method for second order elliptic problems","volume":"83","author":"Wang","year":"2014","journal-title":"Math Comput"},{"issue":"2","key":"10.1016\/j.cnsns.2026.109902_bib0010","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1093\/imanum\/drv012","article-title":"Weak galerkin method for the coupled darcy-stokes flow","volume":"36","author":"Chen","year":"2016","journal-title":"IMA J Numer Anal"},{"key":"10.1016\/j.cnsns.2026.109902_bib0011","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.cam.2018.08.022","article-title":"A weak Galerkin finite element method for the navier-stokes equations","volume":"362","author":"Hu","year":"2019","journal-title":"J Comput Appl Math"},{"issue":"3","key":"10.1016\/j.cnsns.2026.109902_bib0012","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1002\/num.21855","article-title":"Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes","volume":"30","author":"Mu","year":"2014","journal-title":"Numer Methods Partial Differ Equ"},{"issue":"3","key":"10.1016\/j.cnsns.2026.109902_bib0013","doi-asserted-by":"crossref","first-page":"1228","DOI":"10.1093\/imanum\/dru026","article-title":"A new weak galerkin finite element method for the helmholtz equation","volume":"35","author":"Mu","year":"2015","journal-title":"IMA J Numer Anal"},{"issue":"1","key":"10.1016\/j.cnsns.2026.109902_bib0014","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1002\/num.21905","article-title":"Shape regularity conditions for polygonal\/polyhedral meshes, exemplified in a discontinuous galerkin discretization","volume":"31","author":"Mu","year":"2015","journal-title":"Numer Methods Partial Differ Equ"},{"issue":"1","key":"10.1016\/j.cnsns.2026.109902_bib0015","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10444-015-9415-2","article-title":"A weak Galerkin finite element method for the stokes equations","volume":"42","author":"Wang","year":"2016","journal-title":"Adv Comput Math"},{"key":"10.1016\/j.cnsns.2026.109902_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2020.113038","article-title":"Weak Galerkin finite element with curved edges","volume":"381","author":"Mu","year":"2021","journal-title":"J Comput Appl Math"},{"issue":"2","key":"10.1016\/j.cnsns.2026.109902_bib0017","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1051\/m2an\/2018052","article-title":"The virtual element method with curved edges","volume":"53","author":"Veiga","year":"2019","journal-title":"ESAIM Math Modell Numer Anal"},{"key":"10.1016\/j.cnsns.2026.109902_bib0018","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.camwa.2023.11.013","article-title":"Curved elements in weak galerkin finite element methods","volume":"153","author":"Li","year":"2024","journal-title":"Comput Math Appl"},{"key":"10.1016\/j.cnsns.2026.109902_bib0019","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.4208\/cicp.OA-2022-0106","article-title":"A weak Galerkin mixed finite element method for second order elliptic equations on 2D curved domains","volume":"32","author":"Liu","year":"2022","journal-title":"Commun Comput Phys"},{"issue":"120","key":"10.1016\/j.cnsns.2026.109902_bib0020","first-page":"869","article-title":"Projection methods for dirichlet\u2019s problem in approximating polygonal domains with boundary-value corrections","volume":"26","author":"Bramble","year":"1972","journal-title":"Math Comput"},{"issue":"310","key":"10.1016\/j.cnsns.2026.109902_bib0021","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1090\/mcom\/3240","article-title":"A cut finite element method with boundary value correction","volume":"87","author":"Burman","year":"2018","journal-title":"Math Comput"},{"key":"10.1016\/j.cnsns.2026.109902_bib0022","series-title":"European conference on numerical mathematics and advanced applications","first-page":"183","article-title":"A cut finite element method with boundary value correction for the incompressible stokes equations","author":"Burman","year":"2017"},{"issue":"1","key":"10.1016\/j.cnsns.2026.109902_bib0023","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s10543-019-00773-4","article-title":"Dirichlet boundary value correction using lagrange multipliers","volume":"60","author":"Burman","year":"2020","journal-title":"BIT Numer Math"},{"issue":"2","key":"10.1016\/j.cnsns.2026.109902_bib0024","first-page":"391","article-title":"High order VEM on curved domains","volume":"30","author":"Bertoluzza","year":"2019","journal-title":"Rend Lincei-Mat Appl"},{"issue":"319","key":"10.1016\/j.cnsns.2026.109902_bib0025","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1090\/mcom\/3415","article-title":"Optimally accurate higher-order finite element methods for polytopial approximations of domains with smooth boundaries","volume":"88","author":"Cheung","year":"2019","journal-title":"Math Comput"},{"key":"10.1016\/j.cnsns.2026.109902_bib0026","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2020.113341","article-title":"The second-generation shifted boundary method and its numerical analysis","volume":"372","author":"Atallah","year":"2020","journal-title":"Comput Methods Appl Mech Eng"},{"key":"10.1016\/j.cnsns.2026.109902_bib0027","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1016\/j.jcp.2017.10.026","article-title":"The shifted boundary method for embedded domain computations. part i: poisson and stokes problems","volume":"372","author":"Main","year":"2018","journal-title":"J Comput Phys"},{"key":"10.1016\/j.cnsns.2026.109902_bib0028","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1016\/j.jcp.2018.01.023","article-title":"The shifted boundary method for embedded domain computations. part II: linear advection-diffusion and incompressible navier-stokes equations","volume":"372","author":"Main","year":"2018","journal-title":"J Comput Phys"},{"key":"10.1016\/j.cnsns.2026.109902_bib0029","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.114885","article-title":"The high-order shifted boundary method and its analysis","volume":"394","author":"Atallah","year":"2022","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"3","key":"10.1016\/j.cnsns.2026.109902_bib0030","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-024-02552-y","article-title":"A high-order shifted boundary virtual element method for poisson equations on 2d curved domains","volume":"99","author":"Hou","year":"2024","journal-title":"J Sci Comput"},{"key":"10.1016\/j.cnsns.2026.109902_bib0031","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.apnum.2025.08.001","article-title":"A boundary-corrected weak galerkin mixed finite method for elliptic interface problems with curved interfaces","volume":"218","author":"Hou","year":"2025","journal-title":"Appl Numer Math"},{"issue":"1","key":"10.1016\/j.cnsns.2026.109902_bib0032","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1137\/100805200","article-title":"Solving dirichlet boundary-value problems on curved domains by extensions from subdomains","volume":"34","author":"Cockburn","year":"2012","journal-title":"SIAM J Sci Comput"},{"key":"10.1016\/j.cnsns.2026.109902_bib0033","series-title":"\u00dcber ein variationsprinzip zur l\u00f6sung von dirichlet-problemen bei verwendung von teilr\u00e4umen, die keinen randbedingungen unterworfen sind","volume":"vol. 36","author":"Nitsche","year":"1971"},{"issue":"5","key":"10.1016\/j.cnsns.2026.109902_bib0034","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1016\/0898-1221(83)90126-8","article-title":"On finite element approximations of problems having inhomogeneous essential boundary conditions","volume":"9","author":"Fix","year":"1983","journal-title":"Comput Math Appl"},{"key":"10.1016\/j.cnsns.2026.109902_bib0035","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.cam.2015.02.001","article-title":"A weak Galerkin finite element method with polynomial reduction","volume":"285","author":"Mu","year":"2015","journal-title":"J Comput Appl Math"},{"key":"10.1016\/j.cnsns.2026.109902_bib0036","series-title":"Tech. Rep.","article-title":"Weak Garlerkin finite element for curved regions","author":"Pang","year":"2020"},{"issue":"331","key":"10.1016\/j.cnsns.2026.109902_bib0037","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1090\/mcom\/3641","article-title":"Analysis of the shifted boundary method for the poisson problem in domains with corners","volume":"90","author":"Atallah","year":"2021","journal-title":"Math Comput"},{"key":"10.1016\/j.cnsns.2026.109902_bib0038","series-title":"Sobolev spaces","author":"Adams","year":"2003"},{"issue":"207","key":"10.1016\/j.cnsns.2026.109902_bib0039","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1994-1242055-6","article-title":"A robust finite element method for nonhomogeneous dirichlet problems in domains with curved boubdaries","volume":"63","author":"Bramble","year":"1994","journal-title":"Math Comput"},{"key":"10.1016\/j.cnsns.2026.109902_bib0040","series-title":"The mathematical theory of finite element methods","volume":"vol. 3","author":"Brenner","year":"2008"},{"key":"10.1016\/j.cnsns.2026.109902_bib0041","series-title":"Polymesher: a general-purpose mesh generator for polygonal elements written in matlab","first-page":"309","volume":"vol. 45","author":"Talischi","year":"2012"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426002625?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426002625?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T10:53:21Z","timestamp":1778583201000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426002625"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":41,"alternative-id":["S1007570426002625"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.109902","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Weak Galerkin method with boundary value correction","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.109902","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"109902"}}