{"id":"https://openalex.org/W1833891341","doi":"https://doi.org/10.1137/140973955","title":"A Posteriori Error Estimation of $hp$-$dG$ Finite Element Methods for Highly Indefinite Helmholtz Problems","display_name":"A Posteriori Error Estimation of $hp$-$dG$ Finite Element Methods for Highly Indefinite Helmholtz Problems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1833891341","doi":"https://doi.org/10.1137/140973955","mag":"1833891341"},"language":"en","primary_location":{"id":"doi:10.1137/140973955","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140973955","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/A5049235940","display_name":"Stefan Sauter","orcid":"https://orcid.org/0000-0002-1403-1874"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. Sauter","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003697468","display_name":"Jakob Zech","orcid":"https://orcid.org/0000-0003-3163-3735"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Zech","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049235940"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3344,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.60566086,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"53","issue":"5","first_page":"2414","last_page":"2440"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9984999895095825,"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":0.7957934141159058},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7658689618110657},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7291707992553711},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7009783387184143},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.6531292796134949},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6253525018692017},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5893561244010925},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5779306888580322},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5110453367233276},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35726284980773926},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29663121700286865},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.1021241545677185}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7957934141159058},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7658689618110657},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7291707992553711},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7009783387184143},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.6531292796134949},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6253525018692017},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5893561244010925},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5779306888580322},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5110453367233276},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35726284980773926},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29663121700286865},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.1021241545677185},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140973955","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140973955","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W94458352","https://openalex.org/W1966768630","https://openalex.org/W1967469744","https://openalex.org/W1970622200","https://openalex.org/W1978549505","https://openalex.org/W1989594010","https://openalex.org/W2003803951","https://openalex.org/W2004475615","https://openalex.org/W2013150797","https://openalex.org/W2029342920","https://openalex.org/W2029966922","https://openalex.org/W2030028670","https://openalex.org/W2030591225","https://openalex.org/W2032941427","https://openalex.org/W2037092148","https://openalex.org/W2038870672","https://openalex.org/W2056470693","https://openalex.org/W2064309072","https://openalex.org/W2071928229","https://openalex.org/W2072912212","https://openalex.org/W2077458918","https://openalex.org/W2087828859","https://openalex.org/W2089529683","https://openalex.org/W2091907831","https://openalex.org/W2100588850","https://openalex.org/W2122602456","https://openalex.org/W2130552965","https://openalex.org/W2150789707","https://openalex.org/W2150892223","https://openalex.org/W2156154693","https://openalex.org/W2165091991","https://openalex.org/W2168644075"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W4365420316","https://openalex.org/W3176862315","https://openalex.org/W3120022531","https://openalex.org/W2593412144","https://openalex.org/W4251527069"],"abstract_inverted_index":{"In":[0,60],"this":[1],"paper,":[2],"we":[3],"will":[4,32,92],"consider":[5],"an":[6,34],"$hp$-finite":[7],"elements":[8],"discretization":[9,55,80],"of":[10,98],"a":[11,35,85],"highly":[12],"indefinite":[13,70],"Helmholtz":[14],"problem":[15],"by":[16,27],"some":[17],"${dG}$-formulation":[18,73],"which":[19,45],"is":[20,74],"based":[21],"on":[22],"the":[23,51,54,63,72,78,94,99],"ultra-weak":[24],"variational":[25],"formulation":[26],"Cessenat":[28],"and":[29,39,42,53,58,77,96],"Depr\u00e9s.":[30],"We":[31],"introduce":[33],"posteriori":[36],"error":[37],"estimator":[38],"derive":[40],"reliability":[41],"efficiency":[43,95],"estimates":[44],"are":[46],"explicit":[47],"with":[48],"respect":[49],"to":[50,62],"wavenumber":[52],"parameters":[56],"$h$":[57],"$p$.":[59],"contrast":[61],"conventional":[64],"conforming":[65],"finite":[66],"element":[67],"method":[68],"for":[69],"problems,":[71],"unconditionally":[75],"stable":[76],"adaptive":[79],"process":[81],"may":[82],"start":[83],"from":[84],"very":[86],"coarse":[87],"initial":[88],"mesh.":[89],"Numerical":[90],"experiments":[91],"illustrate":[93],"robustness":[97],"method.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
