{"id":"https://openalex.org/W2510636393","doi":"https://doi.org/10.1137/14099810x","title":"Uniformly Stable Discontinuous Galerkin Discretization and Robust Iterative Solution Methods for the Brinkman Problem","display_name":"Uniformly Stable Discontinuous Galerkin Discretization and Robust Iterative Solution Methods for the Brinkman Problem","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2510636393","doi":"https://doi.org/10.1137/14099810x","mag":"2510636393"},"language":"en","primary_location":{"id":"doi:10.1137/14099810x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14099810x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5014378909","display_name":"Qingguo Hong","orcid":"https://orcid.org/0000-0003-2420-9653"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qingguo Hong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5088656822","display_name":"Johannes Kraus","orcid":"https://orcid.org/0000-0003-2261-599X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Johannes Kraus","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014378909"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7357,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.8910694,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"54","issue":"5","first_page":"2750","last_page":"2774"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.998199999332428,"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/T10514","display_name":"Numerical methods in engineering","score":0.9957000017166138,"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":0.8644707798957825},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7899705767631531},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6071162223815918},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5633692741394043},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5005555152893066},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.49831414222717285},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4308483302593231},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41761982440948486},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3069870173931122},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.29718124866485596},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23993775248527527}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8644707798957825},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7899705767631531},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6071162223815918},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5633692741394043},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5005555152893066},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.49831414222717285},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4308483302593231},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41761982440948486},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3069870173931122},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.29718124866485596},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23993775248527527},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/14099810x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14099810x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4571148005","display_name":null,"funder_award_id":"P22989","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1530115438","https://openalex.org/W1966513386","https://openalex.org/W1982954693","https://openalex.org/W1984471539","https://openalex.org/W1985506636","https://openalex.org/W1986520802","https://openalex.org/W1988719701","https://openalex.org/W2002055830","https://openalex.org/W2008522154","https://openalex.org/W2008844677","https://openalex.org/W2014630948","https://openalex.org/W2017085690","https://openalex.org/W2018963986","https://openalex.org/W2022708755","https://openalex.org/W2024706945","https://openalex.org/W2034955757","https://openalex.org/W2038732088","https://openalex.org/W2047397639","https://openalex.org/W2051751432","https://openalex.org/W2053295724","https://openalex.org/W2054937078","https://openalex.org/W2130350269","https://openalex.org/W2139155801","https://openalex.org/W2316118679"],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2182328658","https://openalex.org/W1519938374","https://openalex.org/W84272617","https://openalex.org/W613282331","https://openalex.org/W2092341060","https://openalex.org/W2625595466","https://openalex.org/W2055696851","https://openalex.org/W2162026849","https://openalex.org/W2394687667"],"abstract_inverted_index":{"We":[0,15,45,70],"consider":[1],"robust":[2,76],"iterative":[3],"methods":[4,65],"for":[5,21,54],"discontinuous":[6],"Galerkin":[7],"(DG)":[8],"$H(div,\\Omega)$-conforming":[9],"discretizations":[10],"of":[11,24,31,50,83,91],"the":[12,22,29,47,51,84,87,92],"Brinkman":[13,88],"equations.":[14],"describe":[16],"a":[17,32],"simple":[18],"Uzawa":[19],"iteration":[20],"solution":[23,30],"this":[25],"problem,":[26],"which":[27],"requires":[28],"nearly":[33],"incompressible":[34],"linear":[35],"elasticity":[36],"type":[37],"equation":[38],"with":[39,66],"mass":[40],"term":[41],"on":[42],"every":[43],"iteration.":[44],"prove":[46,71],"uniform":[48],"stability":[49],"DG":[52],"discretization":[53],"both":[55],"problems.":[56],"Then,":[57],"we":[58],"analyze":[59],"variable":[60],"V-cycle":[61],"and":[62,77,90],"W-cycle":[63],"multigrid":[64],"nonnested":[67],"bilinear":[68],"forms.":[69],"that":[72],"these":[73],"algorithms":[74],"are":[75,81],"their":[78],"convergence":[79],"rates":[80],"independent":[82],"parameters":[85],"in":[86],"problem":[89],"mesh":[93],"size.":[94],"The":[95],"theoretical":[96],"analysis":[97],"is":[98],"confirmed":[99],"by":[100],"numerical":[101],"results.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}