{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T22:20:34Z","timestamp":1776205234575,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T00:00:00Z","timestamp":1695945600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T00:00:00Z","timestamp":1695945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2023,10]]},"DOI":"10.1007\/s40314-023-02438-z","type":"journal-article","created":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T17:01:51Z","timestamp":1696006911000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A weak Galerkin finite-element method for singularly perturbed convection\u2013diffusion\u2013reaction problems with interface"],"prefix":"10.1007","volume":"42","author":[{"given":"Tazuddin","family":"Ahmed","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rashmita","family":"Baruah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raman","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,29]]},"reference":[{"issue":"1\u20133","key":"2438_CR1","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0045-7825(82)90071-8","volume":"32","author":"AN Brooks","year":"1982","unstructured":"Brooks AN, Hughes TJR (1982) Streamline upwind\/Petrov\u2013Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier\u2013Stokes equations. Comput Methods Appl Mech Eng 32(1\u20133):199\u2013259","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"10","key":"2438_CR2","doi-asserted-by":"publisher","first-page":"2009","DOI":"10.1142\/S0218202514500146","volume":"24","author":"A Cangiani","year":"2014","unstructured":"Cangiani A, Georgoulis EH, Houston P (2014) hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Math Models Methods Appl Sci 24(10):2009\u20132041","journal-title":"Math Models Methods Appl Sci"},{"key":"2438_CR3","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.cam.2016.10.029","volume":"315","author":"G Chen","year":"2017","unstructured":"Chen G, Feng M, Xie X (2017) A robust WG finite element method for convection\u2013diffusion\u2013reaction equations. J Comput Appl Math 315:107\u2013125","journal-title":"J Comput Appl Math"},{"key":"2438_CR4","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719208","volume-title":"The finite element method for elliptic problems","author":"PG Ciarlet","year":"2002","unstructured":"Ciarlet PG (2002) The finite element method for elliptic problems. SIAM, Philadelphia"},{"key":"2438_CR5","doi-asserted-by":"crossref","unstructured":"Deka B (2018) A weak Galerkin finite element method for elliptic interface problems with polynomial reduction. Numer Math Theory Methods Appl 11(3)","DOI":"10.4208\/nmtma.2017-OA-0078"},{"key":"2438_CR6","doi-asserted-by":"publisher","first-page":"624","DOI":"10.1016\/j.cam.2018.05.034","volume":"344","author":"H Dong","year":"2018","unstructured":"Dong H, Ying W, Zhang J (2018) A hybridizable discontinuous Galerkin method for elliptic interface problems in the formulation of boundary integral equations. J Comput Appl Math 344:624\u2013639","journal-title":"J Comput Appl Math"},{"key":"2438_CR7","unstructured":"Hughes TJR (1979) A multidimentional upwind scheme with no crosswind diffusion. In: Finite element methods for convection dominated flows, AMD, p 34"},{"issue":"2","key":"2438_CR8","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1002\/nme.4382","volume":"93","author":"LNT Huynh","year":"2013","unstructured":"Huynh LNT, Nguyen NC, Peraire J, Khoo BC (2013) A high-order hybridizable discontinuous Galerkin method for elliptic interface problems. Int J Numer Meth Eng 93(2):183\u2013200","journal-title":"Int J Numer Meth Eng"},{"key":"2438_CR9","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.cma.2018.03.011","volume":"337","author":"A Khan","year":"2018","unstructured":"Khan A, Upadhyay CS, Gerritsma M (2018) Spectral element method for parabolic interface problems. Comput Methods Appl Mech Eng 337:66\u201394","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"4","key":"2438_CR10","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1137\/0731054","volume":"31","author":"RJ LeVeque","year":"1994","unstructured":"LeVeque RJ, Zhilin L (1994) The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J Numer Anal 31(4):1019\u20131044","journal-title":"SIAM J Numer Anal"},{"key":"2438_CR11","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717464","volume-title":"The immersed interface method: numerical solutions of PDEs involving interfaces and irregular domains","author":"Z Li","year":"2006","unstructured":"Li Z, Ito K (2006) The immersed interface method: numerical solutions of PDEs involving interfaces and irregular domains. SIAM, Philadelphia"},{"issue":"9\u201310","key":"2438_CR12","first-page":"1061","volume":"192","author":"T Lin","year":"2003","unstructured":"Lin T (2003) Layer-adapted meshes for convection-diffusion problems. Comput Methods Appl Mech Eng 192(9\u201310):1061\u20131105","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2438_CR13","volume-title":"Layer-adapted meshes for reaction-convection-diffusion problems","author":"T Lin","year":"2009","unstructured":"Lin T (2009) Layer-adapted meshes for reaction-convection-diffusion problems. Springer, Berlin"},{"issue":"1","key":"2438_CR14","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s10915-014-9964-4","volume":"65","author":"M Lin","year":"2015","unstructured":"Lin M, Wang J, Ye X, Zhang S (2015) A weak Galerkin finite element method for the Maxwell equations. J Sci Comput 65(1):363\u2013386","journal-title":"J Sci Comput"},{"key":"2438_CR15","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.jcp.2016.08.024","volume":"325","author":"M Lin","year":"2016","unstructured":"Lin M, Wang J, Ye X, Zhao S (2016) A new weak Galerkin finite element method for elliptic interface problems. J Comput Phys 325:157\u2013173","journal-title":"J Comput Phys"},{"issue":"3","key":"2438_CR16","doi-asserted-by":"publisher","first-page":"1482","DOI":"10.1137\/17M1152528","volume":"56","author":"R Lin","year":"2018","unstructured":"Lin R, Ye X, Zhang S, Zhu P (2018) A weak Galerkin finite element method for singularly perturbed convection-diffusion-reaction problems. SIAM J Numer Anal 56(3):1482\u20131497","journal-title":"SIAM J Numer Anal"},{"key":"2438_CR17","doi-asserted-by":"publisher","DOI":"10.1142\/2933","volume-title":"Fitted numerical methods for singular perturbation problems: error estimates in the maximum norm for linear problems in one and two dimensions","author":"JJH Miller","year":"1996","unstructured":"Miller JJH, O\u2019riordan E, Shishkin GI (1996) Fitted numerical methods for singular perturbation problems: error estimates in the maximum norm for linear problems in one and two dimensions. World scientific, Singapore"},{"issue":"3","key":"2438_CR18","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/0021-9991(77)90100-0","volume":"25","author":"CS Peskin","year":"1977","unstructured":"Peskin CS (1977) Numerical analysis of blood flow in the heart. J Comput Phys 25(3):220\u2013252","journal-title":"J Comput Phys"},{"issue":"2","key":"2438_CR19","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/0021-9991(89)90213-1","volume":"81","author":"CS Peskin","year":"1989","unstructured":"Peskin CS, McQueen DM (1989) A three-dimensional computational method for blood flow in the heart i. immersed elastic fibers in a viscous incompressible fluid. J Comput Phys 81(2):372\u2013405","journal-title":"J Comput Phys"},{"issue":"5","key":"2438_CR20","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1002\/(SICI)1521-4001(199805)78:5<291::AID-ZAMM291>3.0.CO;2-R","volume":"78","author":"H-G Roos","year":"1998","unstructured":"Roos H-G (1998) Layer-adapted grids for singular perturbation problems. ZAMM J Appl Math Mech\/Z Angew Math Mech Appl Math Mech 78(5):291\u2013309","journal-title":"ZAMM J Appl Math Mech\/Z Angew Math Mech Appl Math Mech"},{"key":"2438_CR21","doi-asserted-by":"crossref","unstructured":"Shishkin GI (1990) Grid approximation of singularly perturbed elliptic and parabolic equations. Second doctorial thesis, Keldysh Institute, Moscow, Russian. Section 19","DOI":"10.1515\/rnam.1989.4.1.69"},{"issue":"12","key":"2438_CR22","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1016\/j.camwa.2014.03.021","volume":"68","author":"C Wang","year":"2014","unstructured":"Wang C, Wang J (2014) An efficient numerical scheme for the Biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes. Comput Math Appl 68(12):2314\u20132330","journal-title":"Comput Math Appl"},{"key":"2438_CR23","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.cam.2012.10.003","volume":"241","author":"J Wang","year":"2013","unstructured":"Wang J, Ye X (2013) A weak Galerkin finite element method for second-order elliptic problems. J Comput Appl Math 241:103\u2013115","journal-title":"J Comput Appl Math"},{"issue":"289","key":"2438_CR24","doi-asserted-by":"publisher","first-page":"2101","DOI":"10.1090\/S0025-5718-2014-02852-4","volume":"83","author":"J Wang","year":"2014","unstructured":"Wang J, Ye X (2014) A weak Galerkin mixed finite element method for second order elliptic problems. Math Comput 83(289):2101\u20132126","journal-title":"Math Comput"},{"issue":"1","key":"2438_CR25","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s10444-015-9415-2","volume":"42","author":"J Wang","year":"2016","unstructured":"Wang J, Ye X (2016) A weak Galerkin finite element method for the Stokes equations. Adv Comput Math 42(1):155\u2013174","journal-title":"Adv Comput Math"},{"key":"2438_CR26","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.apnum.2018.12.005","volume":"137","author":"S Xie","year":"2019","unstructured":"Xie S, Zhu P, Wang X (2019) Error analysis of weak Galerkin finite element methods for time-dependent convection\u2013diffusion equations. Appl Numer Math 137:19\u201333","journal-title":"Appl Numer Math"},{"key":"2438_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cam.2016.03.025","volume":"280","author":"T Zhang","year":"2016","unstructured":"Zhang T, Tang L (2016) A weak finite element method for elliptic problems in one space dimension. Appl Math Comput 280:1\u201310","journal-title":"Appl Math Comput"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02438-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-023-02438-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02438-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,23]],"date-time":"2023-12-23T02:39:07Z","timestamp":1703299147000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-023-02438-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,29]]},"references-count":27,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["2438"],"URL":"https:\/\/doi.org\/10.1007\/s40314-023-02438-z","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,29]]},"assertion":[{"value":"23 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 September 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors certify that there is no actual or potential conflict of interest in relation to this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"318"}}