{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T14:21:22Z","timestamp":1783088482186,"version":"3.54.6"},"reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2022YFE03040002"],"award-info":[{"award-number":["2022YFE03040002"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371434"],"award-info":[{"award-number":["12371434"]}],"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":["U25A20200"],"award-info":[{"award-number":["U25A20200"]}],"id":[{"id":"10.13039\/501100001809","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":[[2026,11]]},"DOI":"10.1016\/j.cnsns.2026.110305","type":"journal-article","created":{"date-parts":[[2026,6,7]],"date-time":"2026-06-07T14:31:24Z","timestamp":1780842684000},"page":"110305","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P1","title":["A finite element method for a viscous resistive magnetohydrodynamic model"],"prefix":"10.1016","volume":"162","author":[{"given":"Jiajia","family":"Dai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haojie","family":"Tang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiang","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiaolin","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cnsns.2026.110305_bib0001","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s00211-016-0803-4","article-title":"Stable finite element methods preserving \u2207\u00b7B=0 exactly for MHD models","volume":"135","author":"Hu","year":"2017","journal-title":"Numer Math"},{"key":"10.1016\/j.cnsns.2026.110305_bib0002","series-title":"Finite element methods in linear ideal magnetohydrodynamics","author":"Gruber","year":"1985"},{"issue":"08","key":"10.1016\/j.cnsns.2026.110305_bib0003","first-page":"42","article-title":"Principles of magnetohydrodynamics: with applications to laboratory and astrophysical plasmas","volume":"42","author":"Parker","year":"2005","journal-title":"Choice Rev Online"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110305_bib0004","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s002110000193","article-title":"A stabilized finite element method for the incompressible magnetohydrodynamic equations","volume":"87","author":"Gerbeau","year":"2000","journal-title":"Numer Math"},{"key":"10.1016\/j.cnsns.2026.110305_bib0005","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1002\/num.10067","article-title":"Mixed finite element approximation of an MHD problem involving conducting and insulating regions: the 3D case","volume":"19","author":"Guermond","year":"2003","journal-title":"Numer Methods Partial Differ Equ"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110305_bib0006","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1051\/m2an\/2018006","article-title":"A priori estimates and optimal finite element approximation of the MHD flow in smooth domains","volume":"52","author":"He","year":"2018","journal-title":"ESAIM Math Model Numer Anal"},{"issue":"43","key":"10.1016\/j.cnsns.2026.110305_bib0007","doi-asserted-by":"crossref","first-page":"5867","DOI":"10.1016\/S0045-7825(01)00196-7","article-title":"A finite element method for magnetohydrodynamics","volume":"190","author":"Ben Salah","year":"2001","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110305_bib0008","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1137\/18M1205649","article-title":"A convergent linearized lagrange finite element method for the magneto-hydrodynamic equations in two-dimensional nonsmooth and nonconvex domains","volume":"58","author":"Li","year":"2020","journal-title":"SIAM J Numer Anal"},{"key":"10.1016\/j.cnsns.2026.110305_bib0009","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.apnum.2018.10.013","article-title":"Convergence analysis of an unconditionally energy stable projection scheme for magneto-hydrodynamic equations","volume":"136","author":"Yang","year":"2019","journal-title":"Appl Numer Math"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110305_bib0010","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1051\/m2an\/2022020","article-title":"Optimal error estimates of a Crank-Nicolson finite element projection method for magnetohydrodynamic equations","volume":"56","author":"Wang","year":"2022","journal-title":"ESAIM Math Model Numer Anal"},{"key":"10.1016\/j.cnsns.2026.110305_bib0011","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1090\/S0025-5718-10-02341-0","article-title":"Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations","volume":"79","author":"Ba\u0148as","year":"2010","journal-title":"Math Comput"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110305_bib0012","doi-asserted-by":"crossref","first-page":"2150","DOI":"10.1016\/j.camwa.2020.09.003","article-title":"Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible magnetohydrodynamics equations","volume":"80","author":"Qiu","year":"2020","journal-title":"Comput Math Appl"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110305_bib0013","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S0036142998336424","article-title":"The analysis of a finite element method with streamline diffusion for the compressible Navier\u2013Stokes equations","volume":"38","author":"Liu","year":"2006","journal-title":"SIAM J Numer Anal"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110305_bib0014","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/0021-9991(80)90079-0","article-title":"The effect of nonzero \u2207\u202f\u00b7\u202fB on the numerical solution of the magnetohydrodynamic equations","volume":"35","author":"Brackbill","year":"1980","journal-title":"J Comput Phys"},{"key":"10.1016\/j.cnsns.2026.110305_bib0015","doi-asserted-by":"crossref","first-page":"L63","DOI":"10.1086\/184799","article-title":"Numerical simulations of a magnetically confined jet","volume":"311","author":"Clarke","year":"1986","journal-title":"Astrophys J"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110305_bib0016","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0045-7825(97)00184-9","article-title":"Modeling of electromagnetic absorption\/scattering problems using hp-adaptive finite elements","volume":"152","author":"Demkowicz","year":"1998","journal-title":"Comput Methods Appl Mech Eng"},{"key":"10.1016\/j.cnsns.2026.110305_bib0017","series-title":"Mathematical methods for the magnetohydrodynamics of liquid metals","author":"Gerbeau","year":"2006"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110305_bib0018","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1006\/jcph.2000.6519","article-title":"The \u2207\u00b7B=0 constraint in shock-capturing magnetohydrodynamics codes","volume":"161","author":"T\u00f3th","year":"2000","journal-title":"J Comput Phys"},{"issue":"2, Part 1","key":"10.1016\/j.cnsns.2026.110305_bib0019","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1086\/381051","article-title":"An intercomparison between divergence-cleaning and staggered mesh formulations for numerical magnetohydrodynamics","volume":"602","author":"Balsara","year":"2004","journal-title":"Astrophys J"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110305_bib0020","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1006\/jcph.2001.6961","article-title":"Hyperbolic divergence cleaning for the MHD equations","volume":"175","author":"Dedner","year":"2002","journal-title":"J Comput Phys"},{"key":"10.1016\/j.cnsns.2026.110305_bib0021","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1086\/166684","article-title":"Simulation of magnetohydrodynamic flows: a constrained transport method","volume":"332","author":"Evans","year":"1988","journal-title":"Astrophys J"},{"key":"10.1016\/j.cnsns.2026.110305_bib0022","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.jcp.2014.03.001","article-title":"Finite difference weighted essentially non-oscillatory schemes with constrained transport for ideal magnetohydrodynamics","volume":"268","author":"Christlieb","year":"2014","journal-title":"J Comput Phys"},{"key":"10.1016\/j.cnsns.2026.110305_bib0023","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1086\/381377","article-title":"Second order accurate schemes for magnetohydrodynamics with divergence-free reconstruction","volume":"151","author":"Balsara","year":"2003","journal-title":"Astrophys J Suppl Ser"},{"key":"10.1016\/j.cnsns.2026.110305_bib0024","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF01396415","article-title":"Mixed finite elements in R3","volume":"35","author":"N\u00e9d\u00e9lec","year":"1980","journal-title":"Numer Math"},{"key":"10.1016\/j.cnsns.2026.110305_bib0025","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF01389668","article-title":"A new family of mixed finite elements in R3","volume":"50","author":"N\u00e9d\u00e9lec","year":"1986","journal-title":"Numer Math"},{"key":"10.1016\/j.cnsns.2026.110305_bib0026","series-title":"Mathematical aspects of finite element methods","first-page":"292","article-title":"A mixed finite element method for 2-nd order elliptic problems","author":"Raviart","year":"1977"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110305_bib0027","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1051\/m2an\/2016022","article-title":"Error estimates for a numerical method for the compressible Navier-Stokes system on sufficiently smooth domains","volume":"51","author":"Feireisl","year":"2017","journal-title":"ESAIM Math Model Numer Anal"},{"key":"10.1016\/j.cnsns.2026.110305_bib0028","series-title":"Chapter I - ideal fluids","author":"LANDAU","year":"1987"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110305_bib0029","doi-asserted-by":"crossref","first-page":"2146","DOI":"10.1016\/j.jcp.2007.07.003","article-title":"A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions","volume":"226","author":"Jardin","year":"2007","journal-title":"J Comput Phys"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110305_bib0030","doi-asserted-by":"crossref","first-page":"1790","DOI":"10.1080\/00036811.2023.2268634","article-title":"Unique local weak solutions of the non-resistive MHD equations in homogeneous besov space","volume":"103","author":"Baoquan","year":"2024","journal-title":"Appl Anal"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110305_bib0031","doi-asserted-by":"crossref","first-page":"3827","DOI":"10.1016\/j.jde.2019.04.024","article-title":"Global weak solutions to a two-dimensional compressible MHD equations of viscous non-resistive fluids","volume":"267","author":"Li","year":"2019","journal-title":"J Differ Equ"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110305_bib0032","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1007\/PL00000976","article-title":"On the existence of globally defined weak solutions to the Navier-Stokes equations","volume":"3","author":"Feireisl","year":"2001","journal-title":"J Math Fluid Mech"},{"key":"10.1016\/j.cnsns.2026.110305_bib0033","series-title":"Chapter 3 - conforming finite element methods for second-order problems","volume":"Vol. 4","author":"Ciarlet","year":"1978"},{"key":"10.1016\/j.cnsns.2026.110305_bib0034","series-title":"Mixed finite element methods and applications","volume":"Vol. 44","author":"Boffi","year":"2013"},{"key":"10.1016\/j.cnsns.2026.110305_bib0035","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1017\/S0962492902000041","article-title":"Finite elements in computational electromagnetism","volume":"11","author":"Hiptmair","year":"2002","journal-title":"Acta Numerica"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110305_bib0036","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s10915-025-03125-3","article-title":"Rigorous HHO optimal error estimates and simulation of fitzhugh-nagumo model","volume":"105","author":"Singh","year":"2025","journal-title":"J Sci Comput"},{"key":"10.1016\/j.cnsns.2026.110305_bib0037","isbn-type":"print","article-title":"Finite element methods for Maxwell\u2019s equations","author":"Monk","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/9780191545221"},{"key":"10.1016\/j.cnsns.2026.110305_bib0038","isbn-type":"print","article-title":"Finite element methods for Navier-Stokes equations : theory and algorithms","volume":"Vol. 5","author":"Girault","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/3540157964"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110305_bib0039","article-title":"On stationary solution of viscous compressible MHD equations","volume":"519","author":"Rachid","year":"2023","journal-title":"J Math Anal Appl"},{"issue":"13","key":"10.1016\/j.cnsns.2026.110305_bib0040","article-title":"Global small solutions to the 3D compressible viscous non-resistive MHD system","volume":"33","author":"Jiahong","year":"2023","journal-title":"Math Models Methods Appl Sci"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110305_bib0041","doi-asserted-by":"crossref","DOI":"10.1016\/j.jmaa.2024.128565","article-title":"Well-posedness and blow-up criterion for strong solutions of a class of compressible MHD equations","volume":"539","author":"Meng","year":"2024","journal-title":"J Math Anal Appl"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110305_bib0042","article-title":"Global well-posedness for the three-dimensional full compressible viscous non-resistive MHD system","volume":"24","author":"Yang","year":"2022","journal-title":"J Math Fluid Mech"},{"key":"10.1016\/j.cnsns.2026.110305_bib0043","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.camwa.2023.01.027","article-title":"Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method","volume":"135","author":"Ankur","year":"2023","journal-title":"Comput Math Appl"},{"key":"10.1016\/j.cnsns.2026.110305_bib0044","series-title":"The finite element method for elliptic problems","author":"Ciarlet","year":"1978"},{"key":"10.1016\/j.cnsns.2026.110305_bib0045","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1137\/0710022","article-title":"Curved elements in the finite element method. I","volume":"10","author":"Zl\u00e1mal","year":"1973","journal-title":"SIAM J Numer Anal"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110305_bib0046","doi-asserted-by":"crossref","DOI":"10.1063\/1.2173515","article-title":"Coalescence of magnetic islands, sloshing, and the pressure problem","volume":"13","author":"Knoll","year":"2006","journal-title":"Phys Plasmas"},{"issue":"20","key":"10.1016\/j.cnsns.2026.110305_bib0047","doi-asserted-by":"crossref","first-page":"7649","DOI":"10.1016\/j.jcp.2010.06.018","article-title":"Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods","volume":"229","author":"Shadid","year":"2010","journal-title":"J Comput Phys"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426006623?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426006623?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T13:32:09Z","timestamp":1783085529000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426006623"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":47,"alternative-id":["S1007570426006623"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110305","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A finite element method for a viscous resistive magnetohydrodynamic model","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.2026.110305","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":"110305"}}