{"id":"https://openalex.org/W2101354903","doi":"https://doi.org/10.1090/s0025-5718-2013-02760-3","title":"Multilevel preconditioners for discontinuous Galerkin approximations of elliptic problems with jump coefficients","display_name":"Multilevel preconditioners for discontinuous Galerkin approximations of elliptic problems with jump coefficients","publication_year":2013,"publication_date":"2013-10-30","ids":{"openalex":"https://openalex.org/W2101354903","doi":"https://doi.org/10.1090/s0025-5718-2013-02760-3","mag":"2101354903"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2013-02760-3","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02760-3","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":["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/A5070027067","display_name":"Blanca Ayuso de Dios","orcid":"https://orcid.org/0000-0003-4144-6984"},"institutions":[{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]},{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["ES","SA"],"is_corresponding":false,"raw_author_name":"Blanca Ayuso de Dios","raw_affiliation_strings":["Center for Uncertainty Quantification in Computational Science & Engineering, Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE), King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia","Centre de Recerca Matematica, Campus de Bellaterra, Bellaterra, 08193, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Uncertainty Quantification in Computational Science & Engineering, Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE), King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]},{"raw_affiliation_string":"Centre de Recerca Matematica, Campus de Bellaterra, Bellaterra, 08193, Spain","institution_ids":["https://openalex.org/I4210122226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080980271","display_name":"Michael Holst","orcid":"https://orcid.org/0000-0002-3064-4697"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Holst","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, La Jolla, California 92093"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, La Jolla, California 92093","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036190787","display_name":"Yunrong Zhu","orcid":"https://orcid.org/0000-0002-4706-8382"},"institutions":[{"id":"https://openalex.org/I106969075","display_name":"Idaho State University","ror":"https://ror.org/0162z8b04","country_code":"US","type":"education","lineage":["https://openalex.org/I106969075"]},{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yunrong Zhu","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, La Jolla, California 92093","Department of Mathematics, Idaho State University, Pocatello, Idaho 83209-8085"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, La Jolla, California 92093","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Department of Mathematics, Idaho State University, Pocatello, Idaho 83209-8085","institution_ids":["https://openalex.org/I106969075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074536850","display_name":"Ludmil Zikatanov","orcid":"https://orcid.org/0000-0002-5189-4230"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ludmil Zikatanov","raw_affiliation_strings":["Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2327,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.94032155,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"83","issue":"287","first_page":"1083","last_page":"1120"},"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":0.9997000098228455,"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":0.9973000288009644,"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":0.8139818906784058},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7636585235595703},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5504971742630005},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4936719834804535},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4667627513408661},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35476526618003845},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2324671745300293}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8139818906784058},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7636585235595703},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5504971742630005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4936719834804535},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4667627513408661},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35476526618003845},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2324671745300293},{"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/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":7,"locations":[{"id":"doi:10.1090/s0025-5718-2013-02760-3","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02760-3","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:CiteSeerX.psu:10.1.1.185.2434","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.2434","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ccom.ucsd.edu/%7Emholst/pubs/dist/AHZZ10a.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.227.4674","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.227.4674","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/preprints/dec2010/2356.pdf","raw_type":"text"},{"id":"pmh:oai:boa.unimib.it:10281/218128","is_oa":false,"landing_page_url":"http://hdl.handle.net/10281/218128","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:conservancy.umn.edu:11299/181033","is_oa":false,"landing_page_url":"http://hdl.handle.net/11299/181033","pdf_url":null,"source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Preprint"},{"id":"pmh:oai:cris.unibo.it:11585/384386","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/384386","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/594284","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/594284","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":95,"referenced_works":["https://openalex.org/W12123325","https://openalex.org/W48069542","https://openalex.org/W130124921","https://openalex.org/W136882936","https://openalex.org/W1481923190","https://openalex.org/W1493036607","https://openalex.org/W1506342804","https://openalex.org/W1520166905","https://openalex.org/W1521266979","https://openalex.org/W1530115438","https://openalex.org/W1546004968","https://openalex.org/W1548589512","https://openalex.org/W1844813672","https://openalex.org/W1966869202","https://openalex.org/W1970446082","https://openalex.org/W1970588051","https://openalex.org/W1973061863","https://openalex.org/W1973633019","https://openalex.org/W1979771104","https://openalex.org/W1983110265","https://openalex.org/W1986746311","https://openalex.org/W1988570599","https://openalex.org/W1990319748","https://openalex.org/W1992066344","https://openalex.org/W1992384979","https://openalex.org/W1993578085","https://openalex.org/W1994934002","https://openalex.org/W1995944713","https://openalex.org/W1997831216","https://openalex.org/W1998855908","https://openalex.org/W2003230588","https://openalex.org/W2005297950","https://openalex.org/W2005436751","https://openalex.org/W2006066414","https://openalex.org/W2009985306","https://openalex.org/W2010741636","https://openalex.org/W2017085690","https://openalex.org/W2018074366","https://openalex.org/W2018685527","https://openalex.org/W2021257096","https://openalex.org/W2022811246","https://openalex.org/W2022917069","https://openalex.org/W2041523977","https://openalex.org/W2042248875","https://openalex.org/W2042360643","https://openalex.org/W2042732056","https://openalex.org/W2043107107","https://openalex.org/W2055529081","https://openalex.org/W2062246266","https://openalex.org/W2062839853","https://openalex.org/W2065385312","https://openalex.org/W2073263351","https://openalex.org/W2073529350","https://openalex.org/W2079308547","https://openalex.org/W2081624895","https://openalex.org/W2082804737","https://openalex.org/W2085828843","https://openalex.org/W2087652755","https://openalex.org/W2097060633","https://openalex.org/W2099122713","https://openalex.org/W2105777174","https://openalex.org/W2112829131","https://openalex.org/W2116226692","https://openalex.org/W2116640176","https://openalex.org/W2117293438","https://openalex.org/W2117887684","https://openalex.org/W2126036157","https://openalex.org/W2130350269","https://openalex.org/W2131603166","https://openalex.org/W2134819391","https://openalex.org/W2142467748","https://openalex.org/W2145615852","https://openalex.org/W2145995744","https://openalex.org/W2152605678","https://openalex.org/W2168689291","https://openalex.org/W2169540658","https://openalex.org/W2277276517","https://openalex.org/W2326261353","https://openalex.org/W2415509676","https://openalex.org/W2466926104","https://openalex.org/W2489611073","https://openalex.org/W2557433803","https://openalex.org/W2734747941","https://openalex.org/W2798909945","https://openalex.org/W2950223885","https://openalex.org/W4211153182","https://openalex.org/W4232811608","https://openalex.org/W4240258519","https://openalex.org/W4242960114","https://openalex.org/W4245007249","https://openalex.org/W4247826031","https://openalex.org/W4251483682","https://openalex.org/W4254349521","https://openalex.org/W4285719527","https://openalex.org/W6648639693"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W2120874885","https://openalex.org/W1965109456","https://openalex.org/W2351666715","https://openalex.org/W1967543778","https://openalex.org/W2757332726","https://openalex.org/W2382902960","https://openalex.org/W2244225468","https://openalex.org/W2064065738","https://openalex.org/W2036479502"],"abstract_inverted_index":{"We":[0],"introduce":[1],"and":[2,5,66,92,105,141,156,179,184,187,215],"analyze":[3],"two-level":[4,155,186],"multilevel":[6,188],"preconditioners":[7,86,189],"for":[8,89,153,190],"a":[9,39,62,71,122,145,161,205],"family":[10],"of":[11,19,41,78,83,109,125,169,181,194,207,219],"Interior":[12],"Penalty":[13],"(IP)":[14],"discontinuous":[15],"Galerkin":[16],"(DG)":[17],"discretizations":[18,193],"second":[20],"order":[21],"elliptic":[22,195],"problems":[23,196],"with":[24,98,197],"large":[25],"jumps":[26],"in":[27,51,70,101,117],"the":[28,42,52,59,64,75,79,84,99,102,106,110,118,138,150,170,173,177,201,213,217,220],"diffusion":[29,76,103,139],"coefficient.":[30],"Our":[31],"approach":[32],"to":[33,132,137,144],"IPDG-type":[34],"methods":[35,65],"is":[36,87],"based":[37],"on":[38,74,149,176],"splitting":[40],"DG":[43],"space":[44],"into":[45],"two":[46],"components":[47],"that":[48],"are":[49,130,172],"orthogonal":[50],"energy":[53],"inner":[54],"product":[55],"naturally":[56],"induced":[57],"by":[58,159],"methods.":[60,221],"As":[61],"result,":[63],"their":[67],"analysis":[68,82,171,180],"depend":[69],"crucial":[72],"way":[73],"coefficient":[77,104],"problem.":[80],"The":[81],"proposed":[85],"presented":[88],"both":[90,154],"symmetric":[91],"non-symmetric":[93],"IP":[94],"schemes;":[95],"dealing":[96],"simultaneously":[97],"jump":[100,198],"non-nested":[107],"character":[108],"relevant":[111],"discrete":[112],"spaces":[113],"presents":[114],"additional":[115],"difficulties":[116],"analysis,":[119,202],"which":[120,211],"precludes":[121],"simple":[123],"extension":[124],"existing":[126],"results.":[127],"However,":[128],"we":[129,203],"able":[131],"establish":[133],"robustness":[134],"(with":[135],"respect":[136],"coefficient)":[140],"near-optimality":[142],"(up":[143],"logarithmic":[146],"term":[147],"depending":[148],"mesh":[151],"size)":[152],"BPX-type":[157],"preconditioners,":[158],"using":[160],"more":[162],"refined":[163],"Conjugate":[164],"Gradient":[165],"theory.":[166],"Useful":[167],"by-products":[168],"supporting":[174],"results":[175,210],"construction":[178],"simple,":[182],"efficient":[183],"robust":[185],"non-conforming":[191],"Crouzeix-Raviart":[192],"coefficients.":[199],"Following":[200],"present":[204],"sequence":[206],"detailed":[208],"numerical":[209],"verify":[212],"theory":[214],"illustrate":[216],"performance":[218]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
