{"id":"https://openalex.org/W2196858524","doi":"https://doi.org/10.1090/mcom/3158","title":"Finite element exterior calculus with lower-order terms","display_name":"Finite element exterior calculus with lower-order terms","publication_year":2016,"publication_date":"2016-03-23","ids":{"openalex":"https://openalex.org/W2196858524","doi":"https://doi.org/10.1090/mcom/3158","mag":"2196858524"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3158","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3158","pdf_url":null,"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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1509.06463","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067734351","display_name":"Douglas N. Arnold","orcid":"https://orcid.org/0000-0002-0805-7672"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Douglas Arnold","raw_affiliation_strings":["School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044919327","display_name":"Lizao Li","orcid":"https://orcid.org/0000-0001-7056-3368"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lizao Li","raw_affiliation_strings":["School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":null,"apc_paid":null,"fwci":1.1944,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75843389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"86","issue":"307","first_page":"2193","last_page":"2212"},"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":1.0,"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":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7881779670715332},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7742841243743896},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.7329229116439819},{"id":"https://openalex.org/keywords/vector-laplacian","display_name":"Vector Laplacian","score":0.6973289847373962},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6959242224693298},{"id":"https://openalex.org/keywords/vector-calculus","display_name":"Vector calculus","score":0.6330505609512329},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6067581176757812},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5597351789474487},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4356907308101654},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43153366446495056},{"id":"https://openalex.org/keywords/electromagnetism","display_name":"Electromagnetism","score":0.42763644456863403},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.42455410957336426},{"id":"https://openalex.org/keywords/vector-potential","display_name":"Vector potential","score":0.23724320530891418},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18129673600196838}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7881779670715332},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7742841243743896},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.7329229116439819},{"id":"https://openalex.org/C37312099","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Vector Laplacian","level":4,"score":0.6973289847373962},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6959242224693298},{"id":"https://openalex.org/C5408677","wikidata":"https://www.wikidata.org/wiki/Q200802","display_name":"Vector calculus","level":2,"score":0.6330505609512329},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6067581176757812},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5597351789474487},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4356907308101654},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43153366446495056},{"id":"https://openalex.org/C91748784","wikidata":"https://www.wikidata.org/wiki/Q11406","display_name":"Electromagnetism","level":2,"score":0.42763644456863403},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.42455410957336426},{"id":"https://openalex.org/C2027888","wikidata":"https://www.wikidata.org/wiki/Q521126","display_name":"Vector potential","level":3,"score":0.23724320530891418},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18129673600196838},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/3158","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3158","pdf_url":null,"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:arXiv.org:1509.06463","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1509.06463","pdf_url":"https://arxiv.org/pdf/1509.06463","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.712.2205","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.712.2205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ima.umn.edu/%7Earnold/papers/feeclot.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1509.06463","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1509.06463","pdf_url":"https://arxiv.org/pdf/1509.06463","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3342702153","display_name":"Applications and development of finite element exterior calculus","funder_award_id":"1418805","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7214502276","display_name":null,"funder_award_id":"DMS-1418805","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W136185420","https://openalex.org/W638755902","https://openalex.org/W1775501378","https://openalex.org/W1975782244","https://openalex.org/W2015148405","https://openalex.org/W2040933131","https://openalex.org/W2044450536","https://openalex.org/W2051682834","https://openalex.org/W2061172735","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W2071928229","https://openalex.org/W2087765702","https://openalex.org/W2092859851","https://openalex.org/W2138486270","https://openalex.org/W3103476862","https://openalex.org/W4232597038","https://openalex.org/W4237575966"],"related_works":["https://openalex.org/W4389650649","https://openalex.org/W2064733863","https://openalex.org/W4226052975","https://openalex.org/W4299306347","https://openalex.org/W1488706468","https://openalex.org/W3168011518","https://openalex.org/W2000869071","https://openalex.org/W607253236","https://openalex.org/W2898778744","https://openalex.org/W1985968771"],"abstract_inverted_index":{"The":[0,22],"scalar":[1,34,171],"and":[2,10,74,106,159,173],"vector":[3,43,104,148],"Laplacians":[4],"are":[5,77,152],"basic":[6],"operators":[7,110],"in":[8,32,41,88,154],"physics":[9],"engineering.":[11],"In":[12,47,140],"applications,":[13],"they":[14],"frequently":[15],"show":[16,52],"up":[17],"perturbed":[18],"by":[19,91],"lower-order":[20,67,86,123],"terms.":[21],"effect":[23],"of":[24,61,85],"such":[25,156],"perturbations":[26],"on":[27],"mixed":[28,89,118],"finite":[29],"element":[30],"methods":[31,90],"the":[33,42,62,72,75,93,102,147,170,179],"case":[35,44],"is":[36,45,59],"well":[37],"understood,":[38],"but":[39],"that":[40,116],"not.":[46],"this":[48,142],"paper,":[49],"we":[50,130],"first":[51],"that,":[53],"surprisingly,":[54],"for":[55,125,136,146,169],"certain":[56,66],"elements":[57],"there":[58],"degradation":[60],"convergence":[63],"rates":[64],"with":[65,122],"terms":[68,87,124],"even":[69],"when":[70],"both":[71],"solution":[73],"data":[76],"smooth.":[78],"We":[79,114],"then":[80],"give":[81],"a":[82],"systematic":[83],"analysis":[84],"extending":[92],"Finite":[94],"Element":[95],"Exterior":[96],"Calculus":[97],"(FEEC)":[98],"framework,":[99],"which":[100,151],"contains":[101],"scalar,":[103],"Laplacian,":[105],"many":[107,166],"other":[108],"elliptic":[109],"as":[111,157],"special":[112],"cases.":[113],"prove":[115],"stable":[117,121],"discretization":[119],"remains":[120],"sufficiently":[126],"fine":[127],"discretization.":[128],"Moreover,":[129],"derive":[131],"sharp":[132],"improved":[133],"error":[134],"estimates":[135],"each":[137],"individual":[138],"variable.":[139],"particular,":[141],"yields":[143],"new":[144],"results":[145,164,168],"Laplacian":[149],"problem":[150,172],"useful":[153],"applications":[155],"electromagnetism":[158],"acoustics":[160],"modeling.":[161],"Further,":[162],"our":[163],"imply":[165],"previous":[167],"thus":[174],"unify":[175],"them":[176],"all":[177],"under":[178],"FEEC":[180],"framework.":[181]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}