{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:29Z","timestamp":1740123569584,"version":"3.37.3"},"reference-count":58,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771312"],"award-info":[{"award-number":["11771312"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s10915-020-01272-3","type":"journal-article","created":{"date-parts":[[2020,7,14]],"date-time":"2020-07-14T02:02:21Z","timestamp":1594692141000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["EXtended HDG Methods for Second Order Elliptic Interface Problems"],"prefix":"10.1007","volume":"84","author":[{"given":"Yihui","family":"Han","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huangxin","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Ping","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5592-177X","authenticated-orcid":false,"given":"Xiaoping","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,14]]},"reference":[{"issue":"3","key":"1272_CR1","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF02248021","volume":"5","author":"I Babu\u0161ka","year":"1970","unstructured":"Babu\u0161ka, I.: The finite element method for elliptic equations with discontinuous coefficients. Computing 5(3), 207\u2013213 (1970)","journal-title":"Computing"},{"issue":"1","key":"1272_CR2","first-page":"91","volume":"201","author":"I Babu\u0161ka","year":"2011","unstructured":"Babu\u0161ka, I., Banerjee, U.: Stable generalized finite element method (SGFEM). Comput. Methods Appl. Mech. Eng. 201(1), 91\u2013111 (2011)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"4","key":"1272_CR3","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1137\/0731051","volume":"31","author":"I Babu\u0161ka","year":"1994","unstructured":"Babu\u0161ka, I., Caloz, G., Osborn, J.E.: Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal. 31(4), 945\u2013981 (1994)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1272_CR4","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1137\/100791051","volume":"9","author":"I Babu\u0161ka","year":"2010","unstructured":"Babu\u0161ka, I., Lipton, R.: Optimal local approximation spaces for generalized finite element methods with application to multiscale problems. SIAM J. Multiscale Model. Simul. 9(1), 373\u2013406 (2010)","journal-title":"SIAM J. Multiscale Model. Simul."},{"issue":"3","key":"1272_CR5","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1093\/imanum\/7.3.283","volume":"7","author":"JW Barrett","year":"1987","unstructured":"Barrett, J.W., Elliott, C.M.: Fitted and unfitted finite element methods for elliptic equations with smooth interfaces. IMA J. Numer. Anal. 7(3), 283\u2013300 (1987)","journal-title":"IMA J. Numer. Anal."},{"issue":"4","key":"1272_CR6","doi-asserted-by":"crossref","first-page":"043001","DOI":"10.1088\/0965-0393\/17\/4\/043001","volume":"17","author":"T Belytschko","year":"2009","unstructured":"Belytschko, T., Gracie, R., Ventura, G.: A review of extended\/generalized finite element methods for material modeling. Model. Simul. Mater. Sci. Eng. 17(4), 043001 (2009)","journal-title":"Model. Simul. Mater. Sci. Eng."},{"issue":"1","key":"1272_CR7","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/BF02127700","volume":"6","author":"JH Bramble","year":"1996","unstructured":"Bramble, J.H., King, J.T.: A finite element method for interface problems in domains with smooth boundaries and interfaces. Adv. Comput. Math. 6(1), 109\u2013138 (1996)","journal-title":"Adv. Comput. Math."},{"issue":"4","key":"1272_CR8","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.apnum.2011.01.008","volume":"62","author":"E Burman","year":"2012","unstructured":"Burman, E., Hansbo, P.: Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl. Numer. Math. 62(4), 328\u2013341 (2012)","journal-title":"Appl. Numer. Math."},{"issue":"1","key":"1272_CR9","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1137\/16M1056171","volume":"55","author":"Z Cai","year":"2017","unstructured":"Cai, Z., He, C., Zhang, S.: Discontinuous finite element methods for interface problems: robust a priori and a posteriori error estimates. SIAM J. Numer. Anal. 55(1), 400\u2013418 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"1272_CR10","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1137\/100805133","volume":"49","author":"Z Cai","year":"2011","unstructured":"Cai, Z., Ye, X., Zhang, S.: Discontinuous Galerkin finite element methods for interface problems: A priori and a posteriori error estimations. SIAM J. Numer. Anal. 49, 1761\u20131787 (2011)","journal-title":"SIAM J. Numer. Anal."},{"key":"1272_CR11","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.jcp.2014.10.014","volume":"281","author":"Y Cao","year":"2015","unstructured":"Cao, Y., Chu, Y., He, X., Lin, T.: An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity. J. Comput. Phys. 281, 82\u201395 (2015)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"1272_CR12","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1002\/jcc.21646","volume":"32","author":"D Chen","year":"2011","unstructured":"Chen, D., Chen, Z., Chen, C., Geng, W., Wei, G.: MIBPB: a software package for electrostatic analysis. J. Comput. Chem. 32(4), 756\u2013770 (2011)","journal-title":"J. Comput. Chem."},{"issue":"1","key":"1272_CR13","first-page":"437","volume":"36","author":"H Chen","year":"2015","unstructured":"Chen, H., Li, J., Qiu, W.: Robust a posteriori error estimates for HDG method for convection\u2013diffusion equations. IMA J. Numer. Anal. 36(1), 437\u2013462 (2015)","journal-title":"IMA J. Numer. Anal."},{"key":"1272_CR14","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.jcp.2014.01.042","volume":"264","author":"H Chen","year":"2014","unstructured":"Chen, H., Lu, P., Xu, X.: A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation. J. Comput. Phys. 264, 133\u2013151 (2014)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"1272_CR15","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1007\/s10915-016-0272-z","volume":"70","author":"H Chen","year":"2017","unstructured":"Chen, H., Qiu, W., Shi, K., Solano, M.: A superconvergent HDG method for the Maxwell equations. J. Sci. Comput. 70(3), 1010\u20131029 (2017)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1272_CR16","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s002110050336","volume":"79","author":"Z Chen","year":"1998","unstructured":"Chen, Z., Zou, J.: Finite element methods and their convergence for elliptic and parabolic interface problems. Numer. Math. 79(2), 175\u2013202 (1998)","journal-title":"Numer. Math."},{"issue":"2","key":"1272_CR17","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1137\/070706616","volume":"47","author":"B Cockburn","year":"2009","unstructured":"Cockburn, B., Gopalakrishnan, J., Lazarov, R.: Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47(2), 1319\u20131365 (2009)","journal-title":"SIAM J. Numer. Anal."},{"issue":"274","key":"1272_CR18","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1090\/S0025-5718-2010-02410-X","volume":"80","author":"B Cockburn","year":"2011","unstructured":"Cockburn, B., Gopalakrishnan, J., Nguyen, N.C.: Analysis of HDG methods for Stokes flow. Math. Comput. 80(274), 723\u2013760 (2011)","journal-title":"Math. Comput."},{"issue":"1","key":"1272_CR19","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s10915-010-9359-0","volume":"45","author":"B Cockburn","year":"2010","unstructured":"Cockburn, B., Nguyen, N.C., Peraire, J.: A comparison of HDG methods for Stokes flow. J. Sci. Comput. 45(1), 215\u2013237 (2010)","journal-title":"J. Sci. Comput."},{"issue":"288","key":"1272_CR20","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1090\/S0025-5718-2014-02802-0","volume":"83","author":"B Cockburn","year":"2014","unstructured":"Cockburn, B., Sayas, F.-J.: Divergence-conforming HDG methods for Stokes flows. Math. Comput. 83(288), 1571\u20131598 (2014)","journal-title":"Math. Comput."},{"issue":"1","key":"1272_CR21","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1093\/imanum\/drv071","volume":"37","author":"H Dong","year":"2018","unstructured":"Dong, H., Wang, B., Xie, Z., Wang, L.L.: An unfitted hybridizable discontinuous Galerkin method for the Poisson interface problem and its error analysis. IMA J. Numer. Anal. 37(1), 444\u2013476 (2018)","journal-title":"IMA J. Numer. Anal."},{"issue":"1\u20134","key":"1272_CR22","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/S0378-4754(99)00061-0","volume":"50","author":"RE Ewing","year":"1999","unstructured":"Ewing, R.E., Li, Z., Lin, T., Lin, Y.: The immersed finite volume element methods for the elliptic interface problems. Math. Comput. Simul. 50(1\u20134), 63\u201376 (1999)","journal-title":"Math. Comput. Simul."},{"key":"1272_CR23","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.cma.2015.01.014","volume":"289","author":"V Gupta","year":"2015","unstructured":"Gupta, V., Duarte, C.A., Babu\u0161ka, I., Banerjee, U.: Stable GFEM (SGFEM): improved conditioning and accuracy of GFEM\/XFEM for three-dimensional fracture mechanics. Comput. Methods Appl. Mech. Eng. 289, 355\u2013386 (2015)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"2","key":"1272_CR24","first-page":"1","volume":"72","author":"C G\u00fcrkan","year":"2016","unstructured":"G\u00fcrkan, C., Kronbichler, M., Fern\u00e1ndez-M\u00e9ndez, S.: eXtended hybridizable discontinuous Galerkin with heaviside enrichment for heat bimaterial problems. J. Sci. Comput. 72(2), 1\u201326 (2016)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"1272_CR25","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1007\/s10915-015-0066-8","volume":"66","author":"C G\u00fcrkan","year":"2016","unstructured":"G\u00fcrkan, C., Sala-Lardies, E., Kronbichler, M., Fern\u00e1ndez-M\u00e9ndez, S.: eXtended hybridizable discontinous Galerkin (X-HDG) for void problems. J. Sci. Comput. 66(3), 1313\u20131333 (2016)","journal-title":"J. Sci. Comput."},{"issue":"7","key":"1272_CR26","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1109\/JLT.2002.800371","volume":"20","author":"GR Hadley","year":"2002","unstructured":"Hadley, G.R.: High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners. J. Lightwave Technol. 20(7), 1219 (2002)","journal-title":"J. Lightwave Technol."},{"issue":"47\u201348","key":"1272_CR27","doi-asserted-by":"crossref","first-page":"5537","DOI":"10.1016\/S0045-7825(02)00524-8","volume":"191","author":"A Hansbo","year":"2002","unstructured":"Hansbo, A., Hansbo, P.: An unfitted finite element method, based on Nitsche\u2019s method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191(47\u201348), 5537\u20135552 (2002)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1272_CR28","doi-asserted-by":"crossref","unstructured":"Hesthaven, J.S.: High-order accurate methods in time-domain computational electromagnetics: a review. In: Advances in Imaging and Electron Physics, vol. 127, pp. 59\u2013123. Elsevier (2003)","DOI":"10.1016\/S1076-5670(03)80097-6"},{"issue":"2","key":"1272_CR29","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1006\/jcph.1997.5689","volume":"134","author":"TY Hou","year":"1997","unstructured":"Hou, T.Y., Li, Z., Osher, S., Zhao, H.: A hybrid method for moving interface problems with application to the Hele\u2013Shaw flow. J. Comput. Phys. 134(2), 236\u2013252 (1997)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1272_CR30","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1006\/jdeq.2001.4154","volume":"184","author":"J Huang","year":"2002","unstructured":"Huang, J., Zou, J.: Some new a priori estimates for second-order elliptic and parabolic interface problems. J. Differ. Equ. 184(2), 570\u2013586 (2002)","journal-title":"J. Differ. Equ."},{"issue":"1","key":"1272_CR31","first-page":"145","volume":"7","author":"J Huang","year":"2012","unstructured":"Huang, J., Zou, J.: Uniform a priori estimates for elliptic and static Maxwell interface problems. Discrete Contin. Dyn. Syst. Ser. B (DCDS-B) 7(1), 145\u2013170 (2012)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B (DCDS-B)"},{"issue":"2","key":"1272_CR32","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1002\/nme.4382","volume":"93","author":"LNT Huynh","year":"2013","unstructured":"Huynh, L.N.T., Nguyen, N.C., Peraire, J., Khoo, B.C.: A high-order hybridizable discontinuous Galerkin method for elliptic interface problems. Int. J. Numer. Methods Eng. 93(2), 183\u2013200 (2013)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"2","key":"1272_CR33","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.compfluid.2008.02.003","volume":"38","author":"AT Layton","year":"2009","unstructured":"Layton, A.T.: Using integral equations and the immersed interface method to solve immersed boundary problems with stiff forces. Comput. Fluids 38(2), 266\u2013272 (2009)","journal-title":"Comput. Fluids"},{"issue":"4","key":"1272_CR34","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1137\/0731054","volume":"31","author":"RJ Leveque","year":"1994","unstructured":"Leveque, R.J., Li, Z.: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31(4), 1019\u20131044 (1994)","journal-title":"SIAM J. Numer. Anal."},{"key":"1272_CR35","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.cam.2016.04.027","volume":"307","author":"B Li","year":"2016","unstructured":"Li, B., Xie, X.: Analysis of a family of HDG methods for second order elliptic problems. J. Comput. Appl. Math. 307, 37\u201351 (2016)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"1272_CR36","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1137\/140999268","volume":"54","author":"B Li","year":"2016","unstructured":"Li, B., Xie, X.: BPX preconditioner for nonstandard finite element methods for diffusion problems. SIAM J. Numer. Anal. 54(2), 1147\u20131168 (2016)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"1272_CR37","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.4208\/cicp.scpde14.19s","volume":"19","author":"B Li","year":"2016","unstructured":"Li, B., Xie, X., Zhang, S.: Analysis of a two-level algorithm for HDG methods for diffusion problems. Commun. Comput. Phys. 19(5), 1435\u20131460 (2016)","journal-title":"Commun. Comput. Phys."},{"issue":"1","key":"1272_CR38","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.apnum.2009.08.005","volume":"60","author":"J Li","year":"2010","unstructured":"Li, J., Markus, M.J., Wohlmuth, B.I., Zou, J.: Optimal a priori estimates for higher order finite elements for elliptic interface problems. Appl. Numer. Math. 60(1), 19\u201337 (2010)","journal-title":"Appl. Numer. Math."},{"issue":"3","key":"1272_CR39","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0168-9274(98)00015-4","volume":"27","author":"Z Li","year":"1998","unstructured":"Li, Z.: The immersed interface method using a finite element formulation. Appl. Numer. Math. 27(3), 253\u2013267 (1998)","journal-title":"Appl. Numer. Math."},{"key":"1272_CR40","doi-asserted-by":"crossref","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.: The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, vol. 33. SIAM, Philadelphia (2006)"},{"issue":"4","key":"1272_CR41","doi-asserted-by":"crossref","first-page":"807","DOI":"10.3934\/dcdsb.2007.7.807","volume":"7","author":"T Lin","year":"2007","unstructured":"Lin, T., Lin, Y., Sun, W.: Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems. Discrete Contin. Dyn. Syst. B 7(4), 807\u2013823 (2007)","journal-title":"Discrete Contin. Dyn. Syst. B"},{"issue":"2","key":"1272_CR42","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1137\/130912700","volume":"53","author":"T Lin","year":"2015","unstructured":"Lin, T., Lin, Y., Zhang, X.: Partially penalized immersed finite element methods for elliptic interface problems. SIAM J. Numer. Anal. 53(2), 1121\u20131144 (2015)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"1272_CR43","doi-asserted-by":"crossref","first-page":"3134","DOI":"10.1137\/090763093","volume":"50","author":"R Massjung","year":"2012","unstructured":"Massjung, R.: An unfitted discontinuous Galerkin method applied to elliptic interface problems. SIAM J. Numer. Anal. 50(6), 3134\u20133162 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1272_CR44","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1002\/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J","volume":"46","author":"N Mo\u00ebs","year":"1999","unstructured":"Mo\u00ebs, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46(1), 131\u2013150 (1999)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"9","key":"1272_CR45","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1016\/j.cma.2009.10.007","volume":"199","author":"NC Nguyen","year":"2010","unstructured":"Nguyen, N.C., Peraire, J., Cockburn, B.: A hybridizable discontinuous Galerkin method for Stokes flow. Comput. Methods Appl. Mech. Eng. 199(9), 582\u2013597 (2010)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"4\u20135","key":"1272_CR46","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1002\/nme.3092","volume":"86","author":"S Nicaise","year":"2011","unstructured":"Nicaise, S., Renard, Y., Chahine, E.: Optimal convergence analysis for the extended finite element method. Int. J. Numer. Methods Eng. 86(4\u20135), 528\u2013548 (2011)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"4","key":"1272_CR47","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1007\/s002110200395","volume":"95","author":"M Plum","year":"2003","unstructured":"Plum, M., Wieners, C.: Optimal a priori estimates for interface problems. Numer. Math. 95(4), 735\u2013759 (2003)","journal-title":"Numer. Math."},{"issue":"1\u20133","key":"1272_CR48","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0045-7825(99)00072-9","volume":"181","author":"T Strouboulis","year":"2000","unstructured":"Strouboulis, T., Babu\u0161ka, I., Copps, K.: The design and analysis of the generalized finite element method. Comput. Methods Appl. Mech. Eng. 181(1\u20133), 43\u201369 (2000)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"37\u201340","key":"1272_CR49","doi-asserted-by":"crossref","first-page":"4711","DOI":"10.1016\/j.cma.2005.09.019","volume":"195","author":"T Strouboulis","year":"2006","unstructured":"Strouboulis, T., Babu\u0161ka, I., Hidajat, R.: The generalized finite element method for Helmholtz equation: theory, computation, and open problems. Comput. Methods Appl. Mech. Eng. 195(37\u201340), 4711\u20134731 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"16","key":"1272_CR50","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.jcp.2013.03.064","volume":"247","author":"B Wang","year":"2013","unstructured":"Wang, B., Khoo, B.C.: Hybridizable discontinuous Galerkin method (HDG) for Stokes interface flow. J. Comput. Phys. 247(16), 262\u2013278 (2013)","journal-title":"J. Comput. Phys."},{"key":"1272_CR51","unstructured":"Wang, F., Xiao, Y., Xu, J.: High-order eXtended finite element methods for solving interface problems (2016). arXiv preprint arXiv:1604.06171"},{"key":"1272_CR52","first-page":"1","volume":"2014","author":"Q Wang","year":"2014","unstructured":"Wang, Q., Chen, J.: An unfitted discontinuous Galerkin method for elliptic interface problems. J. Appl. Math. 2014, 1\u20139 (2014)","journal-title":"J. Appl. Math."},{"key":"1272_CR53","unstructured":"Wang, T., Yang, C., Xie, X.: A Nitsche-eXtended finite element method for distributed optimal control problems of elliptic interface equations (2018). arXiv preprint arXiv:1810.02271"},{"key":"1272_CR54","unstructured":"Wu, H., Xiao, Y.: An unfitted hp-interface penalty finite element method for elliptic interface problems (2010). arXiv preprint arXiv:1007.2893"},{"key":"1272_CR55","unstructured":"Xu, J.: Estimate of the convergence rate of finite element solutions to elliptic equations of second order with discontinuous coefficients (2013). arXiv preprint arXiv:1311.4178"},{"key":"1272_CR56","unstructured":"Yang, C., Wang, T., Xie, X.: An interface-unfitted finite element method for elliptic interface optimal control problem. Numerical mathematics: theory, methods and applications, accepted (2018). arXiv:1805.04844v2"},{"issue":"21\u201322","key":"1272_CR57","doi-asserted-by":"crossref","first-page":"2051","DOI":"10.1016\/j.cma.2003.12.044","volume":"193","author":"L Zhang","year":"2004","unstructured":"Zhang, L., Gerstenberger, A., Wang, X., Liu, W.K.: Immersed finite element method. Comput. Methods Appl. Mech. Eng. 193(21\u201322), 2051\u20132067 (2004)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"9","key":"1272_CR58","doi-asserted-by":"crossref","first-page":"3155","DOI":"10.1016\/j.jcp.2009.12.034","volume":"229","author":"S Zhao","year":"2010","unstructured":"Zhao, S.: High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces. J. Comput. Phys. 229(9), 3155\u20133170 (2010)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01272-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-020-01272-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01272-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,13]],"date-time":"2021-07-13T23:19:40Z","timestamp":1626218380000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-020-01272-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7]]},"references-count":58,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["1272"],"URL":"https:\/\/doi.org\/10.1007\/s10915-020-01272-3","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2020,7]]},"assertion":[{"value":"24 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"22"}}