{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:38Z","timestamp":1747198058147,"version":"3.40.5"},"reference-count":32,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2020R1C1C1A01005396","2021R1A2C1003340"],"award-info":[{"award-number":["2020R1C1C1A01005396","2021R1A2C1003340"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we develop a new immersed finite element method (IFEM) for two-phase incompressible Stokes flows. We allow the interface to cut the finite elements.\nOn the noninterface element, the standard Crouzeix\u2013Raviart element and the <jats:inline-formula id=\"j_cmam-2022-0122_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>P<\/m:mi>\n                              <m:mn>0<\/m:mn>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2022-0122_eq_0128.png\"\/>\n                        <jats:tex-math>{P_{0}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> element pair is used.\nOn the interface element, the basis functions developed for scalar interface problems (Kwak et al., An analysis of a broken <jats:inline-formula id=\"j_cmam-2022-0122_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>P<\/m:mi>\n                              <m:mn>1<\/m:mn>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2022-0122_eq_0129.png\"\/>\n                        <jats:tex-math>{P_{1}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-nonconforming finite element method for interface problems, <jats:italic>SIAM J. Numer. Anal.<\/jats:italic> (2010)) are modified in such a way that the coupling between the velocity and pressure variable is different.\nThere are two kinds of basis functions. The first kind of basis satisfies the Laplace\u2013Young condition under the assumption of the continuity of the pressure variable.\nIn the second kind, the velocity is of bubble type and is coupled with the discontinuous pressure, still satisfying the Laplace\u2013Young condition.\nWe remark that in the second kind the pressure variable has two degrees of freedom on each interface element.\nTherefore, our methods can handle the discontinuous pressure case.\nNumerical results including the case of the discontinuous pressure variable are provided.\nWe see optimal convergence orders for all examples.<\/jats:p>","DOI":"10.1515\/cmam-2022-0122","type":"journal-article","created":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T08:21:31Z","timestamp":1682497291000},"page":"49-58","source":"Crossref","is-referenced-by-count":0,"title":["A New Immersed Finite Element Method for Two-Phase Stokes Problems Having Discontinuous Pressure"],"prefix":"10.1515","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0635-2897","authenticated-orcid":false,"given":"Gwanghyun","family":"Jo","sequence":"first","affiliation":[{"name":"Department of Mathematics , Kunsan National University , Gunsan-si , Jeollabuk-do , Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5743-1501","authenticated-orcid":false,"given":"Do Young","family":"Kwak","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences , Korea Advanced Institute of Science and Technology , 291 Daehak-ro , Daejeon , 34141 Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,4,27]]},"reference":[{"key":"2024010712054007814_j_cmam-2022-0122_ref_001","doi-asserted-by":"crossref","unstructured":"S.  Adjerid, N.  Chaabane and T.  Lin,\nAn immersed discontinuous finite element method for Stokes interface problems,\nComput. Methods Appl. Mech. Engrg. 293 (2015), 170\u2013190.","DOI":"10.1016\/j.cma.2015.04.006"},{"key":"2024010712054007814_j_cmam-2022-0122_ref_002","doi-asserted-by":"crossref","unstructured":"S.  Adjerid, N.  Chaabane, T.  Lin and P.  Yue,\nAn immersed discontinuous finite element method for the Stokes problem with a moving interface,\nJ. Comput. Appl. Math. 362 (2019), 540\u2013559.","DOI":"10.1016\/j.cam.2018.07.033"},{"key":"2024010712054007814_j_cmam-2022-0122_ref_003","doi-asserted-by":"crossref","unstructured":"R.  Becker, E.  Burman and P.  Hansbo,\nA Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity,\nComput. Methods Appl. Mech. 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