{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T16:25:13Z","timestamp":1773073513767,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T00:00:00Z","timestamp":1592179200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T00:00:00Z","timestamp":1592179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2022,2]]},"DOI":"10.1007\/s00366-020-01079-8","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T10:02:36Z","timestamp":1592215356000},"page":"679-693","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Magnetohydrodynamics (MHD) simulation via an adaptive element free Galerkin method"],"prefix":"10.1007","volume":"38","author":[{"given":"Zahra","family":"Jannesari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehdi","family":"Tatari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,15]]},"reference":[{"key":"1079_CR1","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1007\/s004660050456","volume":"24","author":"S Atluri","year":"1999","unstructured":"Atluri S, Cho J, Kim H (1999) Analysis of thin beams, using the meshless local Petrov\u2013Galerkin method with generalized moving least squares interpolations. Comput Mech 24:334\u2013347","journal-title":"Comput Mech"},{"key":"1079_CR2","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s004660050296","volume":"21","author":"S Atluri","year":"1998","unstructured":"Atluri S, Zhu T (1998) A modied collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput Mech 21:211\u2013222","journal-title":"Comput Mech"},{"key":"1079_CR3","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1090\/S0025-5718-1985-0777265-X","volume":"44","author":"R Bank","year":"1985","unstructured":"Bank R, Weiser A (1985) Some a posteriori error estimator for elliptic partial differential equations. Math Comput 44:283\u2013301","journal-title":"Math Comput"},{"key":"1079_CR4","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/nme.1620370205","volume":"37","author":"T Belytschko","year":"1994","unstructured":"Belytschko T, Lu Y, Gu L (1994) Element free Galerkin methods. Int J Numer Methods Eng 37:229\u2013256","journal-title":"Int J Numer Methods Eng"},{"key":"1079_CR5","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511755750","volume-title":"The physics of plasmas","author":"T Boyd","year":"2003","unstructured":"Boyd T, Sanderson J (2003) The physics of plasmas. Cambridge University Press, Cambridge"},{"key":"1079_CR6","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1016\/j.cma.2003.12.032","volume":"193","author":"E Burman","year":"2004","unstructured":"Burman E, Hansbo P (2004) Edge stabilization for Galerkin approximations of convection\u2013diffusion\u2013reaction problems. Comput Methods Appl Mech Eng 193:1437\u20131453","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1079_CR7","volume-title":"The finite element method for elliptic problems","author":"P Ciarlet","year":"1978","unstructured":"Ciarlet P (1978) The finite element method for elliptic problems. North-Holland, Amsterdam"},{"key":"1079_CR8","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.aml.2018.10.026","volume":"90","author":"R Cavoretto","year":"2019","unstructured":"Cavoretto R, De Rossi A (2019) Adaptive meshless refinement schemes for RBF-PUM collocation. Appl Math Lett 90:131\u2013138","journal-title":"Appl Math Lett"},{"key":"1079_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2020.01.018","author":"R Cavoretto","year":"2020","unstructured":"Cavoretto R, De Rossi A (2020) A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs. Comoput Math Appl. https:\/\/doi.org\/10.1016\/j.camwa.2020.01.018","journal-title":"Comoput Math Appl"},{"key":"1079_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2019.106178","author":"R Cavoretto","year":"2020","unstructured":"Cavoretto R, De Rossi A (2020) An adaptive LOOCV-based refinement scheme for RBF collocation methods over irregular domains. Appl Math Lett. https:\/\/doi.org\/10.1016\/j.aml.2019.106178","journal-title":"Appl Math Lett"},{"key":"1079_CR11","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s004660050286","volume":"21","author":"H Chung","year":"1998","unstructured":"Chung H, Belytschko T (1998) An error estimate in the EFG method. Comput Mech 21:91\u2013100","journal-title":"Comput Mech"},{"key":"1079_CR12","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.apnum.2017.12.004","volume":"126","author":"M Dehghan","year":"2018","unstructured":"Dehghan M, Abbaszadeh M (2018) A reduced proper orthogonal decomposition (POD) element free Galerkin (POD-EFG) method to simulate two dimensional solute transport problems and error estimate. Appl Numer Math 126:92\u2013112","journal-title":"Appl Numer Math"},{"key":"1079_CR13","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1016\/j.cma.2016.09.008","volume":"311","author":"M Dehghan","year":"2016","unstructured":"Dehghan M, Abbaszadeh M (2016) Proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) meshless method for solving incompressible Navier\u2013Stokes equation. Comput Methods Appl Mech Eng 311:856\u2013888","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1079_CR14","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.apnum.2018.10.004","volume":"137","author":"M Dehghan","year":"2019","unstructured":"Dehghan M, Abbaszadeh M (2019) Error analysis and numerical simulation of magnetohydrodynamics (MHD) equation based on the interpolating element free Galerkin (IEFG) method. Appl Numer Math 137:252\u2013273","journal-title":"Appl Numer Math"},{"key":"1079_CR15","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1007\/s00466-013-0886-z","volume":"52","author":"M Dehghan","year":"2013","unstructured":"Dehghan M, Salehi M (2013) A meshfree weak-strong (MWS) form method for the unsteady magnetohydrodynamic (MHD) ow in pipe with arbitrary wall conductivity. Comput Mech 52:1445\u20131462","journal-title":"Comput Mech"},{"key":"1079_CR16","doi-asserted-by":"crossref","first-page":"2292","DOI":"10.1016\/j.camwa.2015.08.032","volume":"70","author":"M Dehgghan","year":"2015","unstructured":"Dehgghan M, Mohammadi V (2015) The method of variably scaled radial kernels for solving two-dimensional magnetohydrodynamic (MHD) equations using two discretizations: The Crank-Nicolson scheme and the method of lines (MOL). Comput Math Appl 70:2292\u20132315","journal-title":"Comput Math Appl"},{"key":"1079_CR17","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1007\/s00366-017-0505-2","volume":"33","author":"M Dehghan","year":"2017","unstructured":"Dehghan M, Haghjoo-Saniji M (2017) The local radial point interpolation meshless method for solving Maxwell equations. Eng Comput 33:897\u2013918","journal-title":"Eng Comput"},{"key":"1079_CR18","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF01178406","volume":"123","author":"Z Demendy","year":"1997","unstructured":"Demendy Z, Nagy T (1997) A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers. Acta Mech 123:135\u2013149","journal-title":"Acta Mech"},{"key":"1079_CR19","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s004660050403","volume":"23","author":"J Dolbow","year":"1999","unstructured":"Dolbow J, Belytschko T (1999) Numerical integration of the Galerkin weak form in meshfree methods. Comput Mech 23:219\u2013230","journal-title":"Comput Mech"},{"issue":"3","key":"1079_CR20","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF02897874","volume":"5","author":"J Dolbow","year":"1998","unstructured":"Dolbow J, Belytschko T (1998) An introduction to programming the meshless element free Galerkin method. Comput Methods Eng 5(3):207\u2013241","journal-title":"Comput Methods Eng"},{"key":"1079_CR21","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1017\/S0962492900002531","volume":"4","author":"K Eriksson","year":"1995","unstructured":"Eriksson K, Estep D, Hansbo P, Johnson C (1995) Introduction to adaptive methods for differential equations. Acta Numer 4:105\u2013158","journal-title":"Acta Numer"},{"issue":"3","key":"1079_CR22","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1007\/s10915-018-0750-6","volume":"77","author":"P Fu","year":"2018","unstructured":"Fu P, Li F, Xu Y (2018) Globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamic equations. J Sci Comput 77(3):1621\u20131659","journal-title":"J Sci Comput"},{"key":"1079_CR23","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717846","volume-title":"Understanding and implementing the finite element method","author":"M Gockenbach","year":"2006","unstructured":"Gockenbach M (2006) Understanding and implementing the finite element method. SIAM, Philadelphia"},{"key":"1079_CR24","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.compstruc.2004.08.011","volume":"83","author":"T Gratsch","year":"2005","unstructured":"Gratsch T, Bathe K (2005) A posteriori error estimation techniques in practical finite element analysis. Comput Struct 83:235\u2013265","journal-title":"Comput Struct"},{"key":"1079_CR25","unstructured":"Guillet T, Pakmor R, Springel V, Chandrashekar P, Klingenberg C. High-order magnetohydrodynamics for astrophysics with an adaptive mesh refinement discontinuous Galerkin scheme. arXiv:1806.02343"},{"issue":"6","key":"1079_CR26","first-page":"1","volume":"15","author":"J Hartmann","year":"1937","unstructured":"Hartmann J, Lazarus F (1937) Experimental investigations on the flow of mercury in a homogeneous magnetic field. K Dan Vidensk Selsk Mat Fys Medd 15(6):1\u201345","journal-title":"K Dan Vidensk Selsk Mat Fys Medd"},{"key":"1079_CR27","doi-asserted-by":"crossref","first-page":"2337","DOI":"10.1016\/j.apm.2012.05.020","volume":"37","author":"H Hosseinzadeh","year":"2013","unstructured":"Hosseinzadeh H, Dehghan M, Mirzaei D (2013) The boundary elements method for magneto-hydrodynamic (MHD) channel flows at high Hartmann numbers. Appl Math Model 37:2337\u20132351","journal-title":"Appl Math Model"},{"key":"1079_CR28","doi-asserted-by":"crossref","first-page":"8301","DOI":"10.1016\/j.jcp.2009.08.007","volume":"228","author":"P Hsieh","year":"2009","unstructured":"Hsieh P, Yang S (2009) A bubble-stabilized least-squares finite element method for steady MHD duct flow problems at high Hartmann numbers. J Comput Phys 228:8301\u20138320","journal-title":"J Comput Phys"},{"key":"1079_CR29","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1016\/S0045-7825(99)00440-5","volume":"190","author":"V John","year":"2000","unstructured":"John V (2000) A numerical study of a posteriori error estimators for convection\u2013diffusion equations. Comput Methods Appl Mech Eng 190:757\u2013781","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1079_CR30","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.apnum.2016.09.007","volume":"111","author":"M Kamranian","year":"2017","unstructured":"Kamranian M, Dehghan M, Tatari M (2017) An adaptive meshless local Petrov\u2013Galerkin method based on a posteriori error estimation for the boundary layer problems. Appl Numer Math 111:181\u2013196","journal-title":"Appl Numer Math"},{"key":"1079_CR31","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1090\/S0025-5718-1981-0616367-1","volume":"37","author":"P Lancaster","year":"1981","unstructured":"Lancaster P, Salkauskas K (1981) Surface generated by moving least squares methods. Math Comput 37:141\u2013158","journal-title":"Math Comput"},{"issue":"1","key":"1079_CR32","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.jcp.2006.12.010","volume":"225","author":"S Lankalapalli","year":"2007","unstructured":"Lankalapalli S, Flaherty J, Shephard M, Strauss H (2007) An adaptive finite element method for magnetohydrodynamics. J Comput Phys 225(1):363\u2013381","journal-title":"J Comput Phys"},{"key":"1079_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-33287-6","volume-title":"The finite element method, theory, implementation and applications","author":"M Larson","year":"2013","unstructured":"Larson M, Bengzon F (2013) The finite element method, theory, implementation and applications. Springer, Berlin"},{"key":"1079_CR34","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.apm.2018.06.040","volume":"63","author":"X Li","year":"2018","unstructured":"Li X (2018) Three-dimensional complex variable element-free Galerkin method. Appl Math Model 63:148\u2013171","journal-title":"Appl Math Model"},{"issue":"3","key":"1079_CR35","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1016\/j.matcom.2008.01.003","volume":"79","author":"V Nguyen","year":"2008","unstructured":"Nguyen V, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79(3):763\u2013813","journal-title":"Math Comput Simul"},{"key":"1079_CR36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apnum.2010.07.010","volume":"61","author":"F Shakeri","year":"2011","unstructured":"Shakeri F, Dehghan M (2011) A nite volume spectral element method for solving magnetohydrodynamic (MHD) equations. Appl Numer Math 61:1\u201323","journal-title":"Appl Numer Math"},{"issue":"1","key":"1079_CR37","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1017\/S0305004100028139","volume":"49","author":"J Shercliff","year":"1953","unstructured":"Shercliff J (1953) Steady motion of conducting fluids in pipes under the action of transverse magnetic field. Math Proc Camb Philos Soc 49(1):136\u2013144","journal-title":"Math Proc Camb Philos Soc"},{"issue":"4","key":"1079_CR38","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1017\/S0022112062000890","volume":"13","author":"J Shercliff","year":"1962","unstructured":"Shercliff J (1962) Magnetohydrodynamics pipe flow part II, high Hartmaan number. J Fluid Mech 13(4):513\u2013518","journal-title":"J Fluid Mech"},{"key":"1079_CR39","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1006\/jcph.1998.5873","volume":"140","author":"D Schnack","year":"1998","unstructured":"Schnack D, Lottati I, Mikic Z, Satyanarayana P (1998) A finite-volume algorithm for three dimensional magnetohydrodynamics on an unstructured, adaptive grid in axially symmetric geometry. J Comput Phys 140:71\u2013121","journal-title":"J Comput Phys"},{"key":"1079_CR40","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1006\/jcph.1998.6091","volume":"147","author":"H Strauss","year":"1998","unstructured":"Strauss H, Longcope D (1998) An adaptive finite element method for magnetohydrodynamics. J Comput Phys 147:318\u2013336","journal-title":"J Comput Phys"},{"key":"1079_CR41","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1016\/j.jcp.2013.10.056","volume":"258","author":"M Tatari","year":"2014","unstructured":"Tatari M, Ghasemi F (2014) The Galerkin boundary node method for magneto-hydrodynamic (MHD) equation. J Comput Phys 258:634\u2013649","journal-title":"J Comput Phys"},{"issue":"12","key":"1079_CR42","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/S0168-874X(02)00163-4","volume":"39","author":"S Verardi","year":"2003","unstructured":"Verardi S, Machado J, Shiyou Y (2003) The application of interpolating MLS approximations to the analysis of MHD flows. Finite Elem Anal Des 39(12):1173\u20131187","journal-title":"Finite Elem Anal Des"},{"key":"1079_CR43","volume-title":"Introduction to moving least squares (MLS) shape functions","author":"L Yaw","year":"2009","unstructured":"Yaw L (2009) Introduction to moving least squares (MLS) shape functions. Walla Walla University, Washington"},{"key":"1079_CR44","doi-asserted-by":"crossref","first-page":"5625","DOI":"10.1016\/j.physleta.2008.05.088","volume":"372","author":"L Zhang","year":"2008","unstructured":"Zhang L, Ouyang J, Zhang X (2008) The two-level element free Galerkin method for MHD flow at high Hartmann numbers. Phys Lett 372:5625\u20135638","journal-title":"Phys Lett"},{"key":"1079_CR45","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1002\/nme.1620330703","volume":"33","author":"O Zienkiewicz","year":"1992","unstructured":"Zienkiewicz O, Zhu J (1992) The superconvergent path recovery and a posteriori error estimation. Part $$1$$: the recovery technique. Int J Numer Methods Eng 33:1365\u20131382","journal-title":"Int J Numer Methods Eng"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-020-01079-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-020-01079-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-020-01079-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,22]],"date-time":"2022-02-22T01:16:43Z","timestamp":1645492603000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-020-01079-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,15]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["1079"],"URL":"https:\/\/doi.org\/10.1007\/s00366-020-01079-8","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,15]]},"assertion":[{"value":"8 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}