{"id":"https://openalex.org/W2766321273","doi":"https://doi.org/10.1137/16m1082159","title":"A Comparison of Finite Element Spaces for $H$(div) Conforming First-Order System Least Squares","display_name":"A Comparison of Finite Element Spaces for $H$(div) Conforming First-Order System Least Squares","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2766321273","doi":"https://doi.org/10.1137/16m1082159","mag":"2766321273"},"language":"en","primary_location":{"id":"doi:10.1137/16m1082159","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1082159","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5040800672","display_name":"Christopher A. Leibs","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christopher A. Leibs","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008694561","display_name":"Thomas A. Manteuffel","orcid":"https://orcid.org/0000-0002-8897-4146"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas A. Manteuffel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5038783425","display_name":"Steffen M\u00fcnzenmaier","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steffen M\u00fcnzenmaier","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040800672"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16145916,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"5","first_page":"S920","last_page":"S944"},"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":0.9980999827384949,"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":0.9980999827384949,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T13862","display_name":"Soil, Finite Element Methods","score":0.9887999892234802,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8410338163375854},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7598470449447632},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5875322222709656},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5716290473937988},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5466355681419373},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47744518518447876},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4728318154811859},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4670827388763428},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.42846226692199707},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41325700283050537},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30034464597702026},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15093085169792175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8410338163375854},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7598470449447632},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5875322222709656},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5716290473937988},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5466355681419373},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47744518518447876},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4728318154811859},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4670827388763428},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.42846226692199707},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41325700283050537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30034464597702026},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15093085169792175},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1082159","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1082159","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1549835960","https://openalex.org/W1890318585","https://openalex.org/W1972266198","https://openalex.org/W1972268912","https://openalex.org/W1973117158","https://openalex.org/W1976140148","https://openalex.org/W1977661241","https://openalex.org/W1978431441","https://openalex.org/W1979739470","https://openalex.org/W1980401206","https://openalex.org/W1984798776","https://openalex.org/W1992261213","https://openalex.org/W2004848415","https://openalex.org/W2006617763","https://openalex.org/W2006871241","https://openalex.org/W2008004031","https://openalex.org/W2010804587","https://openalex.org/W2023037368","https://openalex.org/W2029277969","https://openalex.org/W2033986961","https://openalex.org/W2059537627","https://openalex.org/W2092741912","https://openalex.org/W2094442825","https://openalex.org/W2125313919","https://openalex.org/W2130460563","https://openalex.org/W2132292023","https://openalex.org/W2167223385","https://openalex.org/W4230108662"],"related_works":["https://openalex.org/W2351083540","https://openalex.org/W2953854768","https://openalex.org/W4231686530","https://openalex.org/W2389690162","https://openalex.org/W2060497234","https://openalex.org/W3185647786","https://openalex.org/W2035968624","https://openalex.org/W2181731670","https://openalex.org/W2039467239","https://openalex.org/W2593550064"],"abstract_inverted_index":{"First-order":[0],"system":[1],"least":[2],"squares":[3],"(FOSLS)":[4],"is":[5,100,149],"a":[6,11,97,131,138],"commonly":[7,55],"used":[8,56],"technique":[9],"in":[10,38],"wide":[12],"range":[13],"of":[14,78,161],"physical":[15],"applications.":[16],"FOSLS":[17],"discretizations":[18],"are":[19,36,60,110,137],"straightforward":[20],"to":[21,64,85],"implement":[22],"and":[23,41,59,82,102,107,140],"offer":[24],"many":[25],"advantages":[26],"over":[27],"traditional":[28,105],"Galerkin":[29],"or":[30,128],"saddle-point":[31],"formulations.":[32,92],"Often,":[33],"these":[34],"problems":[35,109,127,129,152],"formulated":[37],"$H(div)$":[39,90],"spaces":[40],"implemented":[42],"using":[43,157],"$H(div)$-conforming":[44,80],"elements.":[45],"These":[46],"elements":[47,58,84],"have":[48],"fewer":[49],"regularity":[50],"assumptions":[51],"than":[52],"the":[53,75,79],"more":[54,66,142],"$H^1$-conforming":[57,86,134],"therefore":[61],"often":[62],"believed":[63],"be":[65],"suited":[67],"for":[68,89,94,125],"less":[69,113],"regular":[70,114],"problems.":[71],"This":[72],"paper":[73],"compares":[74],"approximation":[76],"properties":[77],"Raviart--Thomas":[81],"Brezzi--Douglas--Marini":[83],"piecewise":[87,135],"polynomials":[88,136],"problem":[91],"Furthermore,":[93],"each":[95],"problem,":[96],"corresponding":[98],"$H^1$-formulation":[99,159],"derived":[101],"compared.":[103],"The":[104,121],"Poisson":[106],"Stokes":[108],"examined":[111],"with":[112],"solutions":[115],"addressed":[116],"by":[117,156],"adaptive":[118],"refinement":[119],"strategies.":[120],"results":[122],"imply":[123],"that":[124],"smooth":[126],"exhibiting":[130],"point":[132],"singularity":[133],"viable,":[139],"sometimes":[141],"efficient,":[143],"choice":[144],"even":[145],"if":[146],"an":[147,158,162],"$H(div)$-formulation":[148],"used.":[150],"Smooth":[151],"do":[153],"additionally":[154],"benefit":[155],"instead":[160],"$H(div)$-formulation.":[163]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
