{"id":"https://openalex.org/W2081729435","doi":"https://doi.org/10.1090/s0025-5718-03-01616-8","title":"A new approximation technique for div-curl systems","display_name":"A new approximation technique for div-curl systems","publication_year":2003,"publication_date":"2003-08-26","ids":{"openalex":"https://openalex.org/W2081729435","doi":"https://doi.org/10.1090/s0025-5718-03-01616-8","mag":"2081729435"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-03-01616-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01616-8","pdf_url":"https://www.ams.org/mcom/2004-73-248/S0025-5718-03-01616-8/S0025-5718-03-01616-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2004-73-248/S0025-5718-03-01616-8/S0025-5718-03-01616-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111580212","display_name":"James H. Bramble","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Bramble","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368","Department of Mathematics, Texas A&M University, College Station, Texas 77843\u20133368"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843\u20133368","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113545293","display_name":"Joseph E. Pasciak","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph Pasciak","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368","Department of Mathematics, Texas A&M University, College Station, Texas 77843\u20133368"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843\u20133368","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2029,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.91204942,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"73","issue":"248","first_page":"1739","last_page":"1762"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T10514","display_name":"Numerical methods in engineering","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6845256090164185},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4934603273868561},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43011370301246643},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.42722100019454956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34293097257614136}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6845256090164185},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4934603273868561},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43011370301246643},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.42722100019454956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34293097257614136}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-03-01616-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01616-8","pdf_url":"https://www.ams.org/mcom/2004-73-248/S0025-5718-03-01616-8/S0025-5718-03-01616-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.100.1291","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.1291","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2004-73-248/S0025-5718-03-01616-8/S0025-5718-03-01616-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.503.1414","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.503.1414","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tamu.edu/~joe.pasciak/papers/divcurl.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.5539","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.5539","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isc.tamu.edu/publications-reports/tr/0301.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-03-01616-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-03-01616-8","pdf_url":"https://www.ams.org/mcom/2004-73-248/S0025-5718-03-01616-8/S0025-5718-03-01616-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5099999904632568,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[{"id":"https://openalex.org/G7371831924","display_name":"Negative Norm Least-Squares Finite Element Methods for Electromagnetics","funder_award_id":"9805590","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8682745120","display_name":"Construction of Accurate, Robust and Efficient Numerical Techniques for Partial Differential Equations","funder_award_id":"9973328","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2081729435.pdf","grobid_xml":"https://content.openalex.org/works/W2081729435.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W169961368","https://openalex.org/W1584365460","https://openalex.org/W1586623601","https://openalex.org/W1852082788","https://openalex.org/W1969732357","https://openalex.org/W1970198065","https://openalex.org/W1983929352","https://openalex.org/W1994183034","https://openalex.org/W2000554621","https://openalex.org/W2001104413","https://openalex.org/W2006895912","https://openalex.org/W2023358451","https://openalex.org/W2025127762","https://openalex.org/W2029384438","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W2065157529","https://openalex.org/W2067527388","https://openalex.org/W2068798260","https://openalex.org/W2071704402","https://openalex.org/W2072247902","https://openalex.org/W2075224881","https://openalex.org/W2091081883","https://openalex.org/W2101109206","https://openalex.org/W2101743932","https://openalex.org/W2199169705","https://openalex.org/W3149667697","https://openalex.org/W4237533267"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421"],"abstract_inverted_index":{"In":[0],"this":[1,104,199,206,221],"paper,":[2],"we":[3,192,223,236],"describe":[4],"an":[5,123],"approximation":[6],"technique":[7],"for":[8,256,383],"div-curl":[9],"systems":[10],"based":[11,197],"in":[12,77,129,186],"<inline-formula":[13,57,78,139,280,326],"content-type=\"math/mathml\">":[14,58,79,140,281,327],"<mml:math":[15,59,80,141,282,328],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16,60,81,142,283,329],"alttext=\"left-parenthesis":[17,143,284],"upper":[18,23,62,83,144,149,285,292],"L":[19,145],"squared":[20,146],"left-parenthesis":[21,147,290],"normal":[22,148,291],"Omega":[24,150,293],"right-parenthesis":[25,151,152,294,295],"cubed":[26],"right-parenthesis\">":[27],"<mml:semantics>":[28,64,86,154,297,337],"<mml:mrow>":[29,155,298,338],"<mml:mo":[30,36,43,47,156,162,168,171,299,305,311,314],"stretchy=\"false\">(</mml:mo>":[31,37,157,163,300,306],"<mml:msup>":[32,42,87,158,170,301,313],"<mml:mi>L</mml:mi>":[33,159],"<mml:mn>2</mml:mn>":[34,160,348],"</mml:msup>":[35,46,94,161,174,304,317],"<mml:mi":[38,65,90,164,307],"mathvariant=\"normal\">":[39,66,165,308],"\u03a9":[40,67,166,309],"</mml:mi>":[41,68,167,310],"stretchy=\"false\">)</mml:mo>":[44,48,169,172,312,315],"<mml:mn>3</mml:mn>":[45,93,173,316],"</mml:mrow>":[49,92,175,318,347,349],"<mml:annotation":[50,69,95,176,319,350],"encoding=\"application/x-tex\">(L^2(\\Omega":[51,177],")^3)</mml:annotation>":[52],"</mml:semantics>":[53,71,98,179,322,354],"</mml:math>":[54,72,99,180,323,355],"</inline-formula>":[55,73,100,181,324,356],"where":[56,134],"alttext=\"normal":[61],"Omega\">":[63],"encoding=\"application/x-tex\">\\Omega</mml:annotation>":[70],"is":[74,138,262,266],"a":[75,107,130,238,245,373],"domain":[76],"alttext=\"double-struck":[82],"R":[84],"cubed\">":[85,153,296],"<mml:mrow":[88,344],"class=\"MJX-TeXAtom-ORD\">":[89,345],"mathvariant=\"double-struck\">R</mml:mi>":[91],"encoding=\"application/x-tex\">\\mathbb":[96],"{R}^3</mml:annotation>":[97],".":[101],"We":[102],"formulate":[103],"problem":[105,110],"as":[106],"general":[108],"variational":[109],"with":[111,258,325],"different":[112],"test":[113,216,226,375],"and":[114,182,217,235,366],"trial":[115,218],"spaces.":[116,190,219],"The":[117,202,358],"analysis":[118],"requires":[119],"the":[120,135,183,209,225,230,381],"verification":[121],"of":[122,205,211,214],"appropriate":[124],"inf-sup":[125,232],"condition.":[126],"This":[127,250],"results":[128,391],"very":[131],"weak":[132,200],"formulation":[133,241],"solution":[136],"space":[137,227,376],"))^3</mml:annotation>":[178,321],"data":[184],"reside":[185],"various":[187],"negative":[188],"norm":[189],"Subsequently,":[191],"consider":[193],"finite":[194],"element":[195],"approximations":[196],"on":[198],"formulation.":[201],"main":[203],"approach":[204,371],"paper":[207],"involves":[208],"development":[210],"\u201cstable":[212],"pairs\"":[213],"discrete":[215,231],"With":[220],"approach,":[222],"enlarge":[224],"so":[228],"that":[229],"condition":[233],"holds":[234],"use":[237],"negative-norm":[239],"least-squares":[240],"to":[242,244,252,268,380],"reduce":[243],"uniquely":[246],"solvable":[247],"linear":[248],"system.":[249],"leads":[251],"optimal":[253],"order":[254],"estimates":[255],"problems":[257,272],"minimal":[259],"regularity":[260,278],"which":[261,377],"important":[263],"since":[264],"it":[265],"possible":[267],"construct":[269],"magnetostatic":[270],"field":[271],"whose":[273],"solutions":[274],"have":[275],"low":[276],"Sobolev":[277],"(e.g.,":[279],"H":[286],"Superscript":[287],"s":[288,332],"Baseline":[289],"<mml:mi>H</mml:mi>":[302],"<mml:mi>s</mml:mi>":[303,341],"encoding=\"application/x-tex\">(H^s(\\Omega":[320],"alttext=\"0":[330],"greater-than":[331,333],"1":[334],"slash":[335],"2\">":[336],"<mml:mn>0</mml:mn>":[339],"<mml:mo>&gt;</mml:mo>":[340,342],"<mml:mn>1</mml:mn>":[343],"<mml:mo>/</mml:mo>":[346],"encoding=\"application/x-tex\">0&gt;":[351],"s&gt;":[352],"1/2</mml:annotation>":[353],").":[357],"resulting":[359],"algebraic":[360],"equations":[361],"are":[362,392],"symmetric,":[363],"positive":[364],"definite":[365],"well":[367],"conditioned.":[368],"A":[369],"second":[370],"using":[372],"smaller":[374],"adds":[378],"terms":[379],"form":[382],"stabilization":[384],"will":[385],"also":[386,393],"be":[387],"mentioned.":[388],"Some":[389],"numerical":[390],"presented.":[394]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
