{"id":"https://openalex.org/W4415397338","doi":"https://doi.org/10.1515/cmam-2025-0046","title":"Error Estimates of Scalar Auxiliary Variable Schemes with Variable Time Steps for the Magneto-Hydrodynamic Equations","display_name":"Error Estimates of Scalar Auxiliary Variable Schemes with Variable Time Steps for the Magneto-Hydrodynamic Equations","publication_year":2025,"publication_date":"2025-10-21","ids":{"openalex":"https://openalex.org/W4415397338","doi":"https://doi.org/10.1515/cmam-2025-0046"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2025-0046","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2025-0046","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071286986","display_name":"Yuguang Mu","orcid":"https://orcid.org/0000-0002-2499-026X"},"institutions":[{"id":"https://openalex.org/I46305995","display_name":"Taiyuan University of Science and Technology","ror":"https://ror.org/01wcbdc92","country_code":"CN","type":"education","lineage":["https://openalex.org/I46305995"]},{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuanyuan Mu","raw_affiliation_strings":["School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China","institution_ids":["https://openalex.org/I9086337","https://openalex.org/I46305995"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Danxia Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I46305995","display_name":"Taiyuan University of Science and Technology","ror":"https://ror.org/01wcbdc92","country_code":"CN","type":"education","lineage":["https://openalex.org/I46305995"]},{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Danxia Wang","raw_affiliation_strings":["School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China","institution_ids":["https://openalex.org/I9086337","https://openalex.org/I46305995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102941557","display_name":"Hongen Jia","orcid":"https://orcid.org/0000-0002-4701-4608"},"institutions":[{"id":"https://openalex.org/I46305995","display_name":"Taiyuan University of Science and Technology","ror":"https://ror.org/01wcbdc92","country_code":"CN","type":"education","lineage":["https://openalex.org/I46305995"]},{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongen Jia","raw_affiliation_strings":["School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China","institution_ids":["https://openalex.org/I9086337","https://openalex.org/I46305995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082488018","display_name":"Chenhui Zhang","orcid":"https://orcid.org/0000-0002-0124-6315"},"institutions":[{"id":"https://openalex.org/I46305995","display_name":"Taiyuan University of Science and Technology","ror":"https://ror.org/01wcbdc92","country_code":"CN","type":"education","lineage":["https://openalex.org/I46305995"]},{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenhui Zhang","raw_affiliation_strings":["School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics , 47846 Taiyuan University of Technology , Taiyuan , 030024, Shanxi , P. R. China","institution_ids":["https://openalex.org/I9086337","https://openalex.org/I46305995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071286986"],"corresponding_institution_ids":["https://openalex.org/I46305995","https://openalex.org/I9086337"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30819392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"1","first_page":"109","last_page":"126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.66839998960495},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.661899983882904},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6459000110626221},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.45579999685287476},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45170000195503235},{"id":"https://openalex.org/keywords/magnetohydrodynamics","display_name":"Magnetohydrodynamics","score":0.4487999975681305},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.3982999920845032}],"concepts":[{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.66839998960495},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.661899983882904},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6459000110626221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.620199978351593},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6008999943733215},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.45579999685287476},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45170000195503235},{"id":"https://openalex.org/C31532427","wikidata":"https://www.wikidata.org/wiki/Q2549249","display_name":"Magnetohydrodynamics","level":3,"score":0.4487999975681305},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C42471609","wikidata":"https://www.wikidata.org/wiki/Q1779048","display_name":"Magnetohydrodynamic drive","level":4,"score":0.3776000142097473},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3614000082015991},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.35019999742507935},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3237999975681305},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.3059999942779541},{"id":"https://openalex.org/C52970973","wikidata":"https://www.wikidata.org/wiki/Q2497134","display_name":"Adaptive system","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2648000121116638}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2025-0046","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2025-0046","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1040216278","display_name":null,"funder_award_id":"2021-029","funder_id":"https://openalex.org/F4320321884","funder_display_name":"Shanxi Scholarship Council of China"},{"id":"https://openalex.org/G1821548215","display_name":null,"funder_award_id":"12301556","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4402535638","display_name":null,"funder_award_id":"12426105","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8350764475","display_name":null,"funder_award_id":"202203021212249","funder_id":"https://openalex.org/F4320322666","funder_display_name":"Natural Science Foundation of Shanxi Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321884","display_name":"Shanxi Scholarship Council of China","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320322666","display_name":"Natural Science Foundation of Shanxi Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W638755902","https://openalex.org/W1480058644","https://openalex.org/W1966483208","https://openalex.org/W2013307001","https://openalex.org/W2030940697","https://openalex.org/W2039750237","https://openalex.org/W2045478774","https://openalex.org/W2047859546","https://openalex.org/W2090708196","https://openalex.org/W2099460886","https://openalex.org/W2110634732","https://openalex.org/W2138371979","https://openalex.org/W2324934537","https://openalex.org/W2497754766","https://openalex.org/W2522294189","https://openalex.org/W2748749923","https://openalex.org/W2766149883","https://openalex.org/W2949368409","https://openalex.org/W2964977327","https://openalex.org/W2966020116","https://openalex.org/W2979590704","https://openalex.org/W3000347973","https://openalex.org/W3002206465","https://openalex.org/W3018009055","https://openalex.org/W3152071472","https://openalex.org/W3170963779","https://openalex.org/W3206494080","https://openalex.org/W4300979639","https://openalex.org/W4301603529","https://openalex.org/W4307260081","https://openalex.org/W4308314981","https://openalex.org/W4313656479","https://openalex.org/W4317640780","https://openalex.org/W4366393036","https://openalex.org/W4382751426","https://openalex.org/W4383551032","https://openalex.org/W4386254128","https://openalex.org/W4401647571"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,105],"paper,":[3],"we":[4,62,109,131,160,167],"employ":[5],"an":[6,113,180],"adaptive":[7,128,182],"time-stepping":[8,129],"strategy":[9],"to":[10,27,81,137,173],"conduct":[11],"a":[12,29,65,83,133,162],"comprehensive":[13],"theoretical":[14,176],"analysis":[15],"and":[16,46],"numerical":[17,30,171],"simulations":[18,172],"of":[19,53,89,122,141,153],"the":[20,34,51,55,59,69,75,95,101,127,139,142,150,157,175],"magnetohydrodynamic":[21],"(MHD)":[22],"system.":[23,143],"Our":[24],"objective":[25],"is":[26,88,117,145],"formulate":[28],"scheme":[31],"based":[32,125],"on":[33,126],"variable":[35,73],"time-steps":[36],"second-order":[37],"backward":[38],"difference":[39],"formula":[40],"(VBDF2),":[41],"which":[42,87],"exhibits":[43],"linear,":[44],"decoupled,":[45],"semi-discrete":[47,134],"properties.":[48],"Firstly,":[49],"considering":[50],"complexity":[52],"handling":[54],"nonlinear":[56,96],"terms":[57,121],"in":[58,92,120],"MHD":[60,102,135],"equations,":[61],"will":[63],"introduce":[64],"method":[66],"that":[67,116],"combines":[68],"exponential":[70],"scalar":[71],"auxiliary":[72,85,107],"with":[74,94],"zero-energy":[76],"contribution.":[77],"This":[78],"allows":[79],"us":[80],"construct":[82],"new":[84,106],"variable,":[86,108],"crucial":[90],"importance":[91],"dealing":[93],"terms.":[97],"Subsequently,":[98],"by":[99,156,178],"reformulating":[100],"system":[103,115,136],"using":[104,179],"have":[110],"successfully":[111],"derived":[112],"equivalent":[114],"unconditionally":[118],"stable":[119],"energy.":[123],"Secondly,":[124],"strategy,":[130],"establish":[132],"guarantee":[138],"stability":[140],"It":[144],"worth":[146],"noting":[147],"that,":[148],"under":[149],"favorable":[151],"condition":[152],"being":[154],"unrestricted":[155],"time-step":[158,183],"size,":[159],"present":[161],"rigorous":[163],"error":[164],"analysis.":[165],"Finally,":[166],"carry":[168],"out":[169],"several":[170],"verify":[174],"results":[177],"effective":[181],"strategy.":[184]},"counts_by_year":[],"updated_date":"2026-04-17T18:11:37.981687","created_date":"2025-10-22T00:00:00"}
