{"id":"https://openalex.org/W3017021094","doi":"https://doi.org/10.1007/s10915-021-01606-9","title":"Inverses of SBP-SAT Finite Difference Operators Approximating the First and Second Derivative","display_name":"Inverses of SBP-SAT Finite Difference Operators Approximating the First and Second Derivative","publication_year":2021,"publication_date":"2021-09-20","ids":{"openalex":"https://openalex.org/W3017021094","doi":"https://doi.org/10.1007/s10915-021-01606-9","mag":"3017021094"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01606-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01606-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01606-9.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01606-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085211887","display_name":"Sofia Eriksson","orcid":"https://orcid.org/0000-0003-1216-1672"},"institutions":[{"id":"https://openalex.org/I223464139","display_name":"Linnaeus University","ror":"https://ror.org/00j9qag85","country_code":"SE","type":"education","lineage":["https://openalex.org/I223464139"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Sofia Eriksson","raw_affiliation_strings":["Department of Mathematics, Linnaeus University, V\u00e4xj\u00f6, Sweden","Linna\u00e9us University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Linnaeus University, V\u00e4xj\u00f6, Sweden","institution_ids":["https://openalex.org/I223464139"]},{"raw_affiliation_string":"Linna\u00e9us University","institution_ids":["https://openalex.org/I223464139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085211887"],"corresponding_institution_ids":["https://openalex.org/I223464139"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00605148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"89","issue":"2","first_page":null,"last_page":null},"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":0.9997000098228455,"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":0.9997000098228455,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9983000159263611,"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/discretization","display_name":"Discretization","score":0.8966586589813232},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.842663049697876},{"id":"https://openalex.org/keywords/summation-by-parts","display_name":"Summation by parts","score":0.6975735425949097},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5427908897399902},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5121905207633972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5087257027626038},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4910116195678711},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47304099798202515},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.44879332184791565},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4190170466899872},{"id":"https://openalex.org/keywords/second-derivative","display_name":"Second derivative","score":0.41365548968315125}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8966586589813232},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.842663049697876},{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.6975735425949097},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5427908897399902},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5121905207633972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5087257027626038},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4910116195678711},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47304099798202515},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.44879332184791565},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4190170466899872},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.41365548968315125},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10915-021-01606-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01606-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01606-9.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2004.08938","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.08938","pdf_url":"https://arxiv.org/pdf/2004.08938","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":"mag:3017021094","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2004.08938.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2004.08938","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.08938","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10915-021-01606-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01606-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01606-9.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323551","display_name":"Linn\u00e9universitetet","ror":"https://ror.org/00j9qag85"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3017021094.pdf","grobid_xml":"https://content.openalex.org/works/W3017021094.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W73160571","https://openalex.org/W1523615189","https://openalex.org/W1538356049","https://openalex.org/W1798338637","https://openalex.org/W1965855805","https://openalex.org/W1972670182","https://openalex.org/W1973468675","https://openalex.org/W1977956169","https://openalex.org/W1978362527","https://openalex.org/W1990297508","https://openalex.org/W1993713305","https://openalex.org/W1995071315","https://openalex.org/W2003586033","https://openalex.org/W2007169649","https://openalex.org/W2024067995","https://openalex.org/W2024742650","https://openalex.org/W2038516134","https://openalex.org/W2046899724","https://openalex.org/W2049991352","https://openalex.org/W2051465806","https://openalex.org/W2065978762","https://openalex.org/W2071447842","https://openalex.org/W2092625275","https://openalex.org/W2109448994","https://openalex.org/W2113972433","https://openalex.org/W2125889036","https://openalex.org/W2154328412","https://openalex.org/W2554572918","https://openalex.org/W2807541158","https://openalex.org/W2975923947","https://openalex.org/W3039534546","https://openalex.org/W3101132641"],"related_works":["https://openalex.org/W1995071315","https://openalex.org/W2596090746","https://openalex.org/W3106024862","https://openalex.org/W1984693670","https://openalex.org/W2049991352","https://openalex.org/W2804791660","https://openalex.org/W2949646628","https://openalex.org/W2936880700","https://openalex.org/W2039536088","https://openalex.org/W2002756386","https://openalex.org/W2996622886","https://openalex.org/W2652027923","https://openalex.org/W2963790346","https://openalex.org/W3029291000","https://openalex.org/W2170729639","https://openalex.org/W1976794551","https://openalex.org/W2063246118","https://openalex.org/W2098907255","https://openalex.org/W2087482474","https://openalex.org/W1971031985"],"abstract_inverted_index":{"Abstract":[0],"The":[1,62,143],"scalar,":[2],"one-dimensional":[3],"advection":[4],"equation":[5,8],"and":[6,56,157],"heat":[7],"are":[9,13,120,164],"considered.":[10],"These":[11],"equations":[12],"discretized":[14],"in":[15],"space,":[16],"using":[17],"a":[18,33],"finite":[19],"difference":[20],"method":[21,35],"satisfying":[22],"summation-by-parts":[23],"(SBP)":[24],"properties.":[25],"To":[26],"impose":[27],"the":[28,50,54,57,70,75,78,103,108,117,124,130,138,162],"boundary":[29],"conditions,":[30],"we":[31,91],"use":[32],"penalty":[34,118],"called":[36],"simultaneous":[37],"approximation":[38],"term":[39],"(SAT).":[40],"Together,":[41],"this":[42,88],"gives":[43],"rise":[44],"to":[45],"two":[46],"semi-discrete":[47,125],"schemes":[48],"where":[49],"discretization":[51,63,79,104,131],"matrices":[52,64,105],"approximate":[53],"first":[55],"second":[58,109,156],"derivative":[59,110],"operators,":[60,161],"respectively.":[61],"depend":[65],"on":[66],"free":[67],"parameters":[68,100,119],"from":[69],"SAT":[71,99],"treatment.":[72],"We":[73],"derive":[74],"inverses":[76,163],"of":[77,98,150,153],"matrices,":[80],"interpreting":[81],"them":[82],"as":[83],"discrete":[84],"Green\u2019s":[85],"functions.":[86],"In":[87,107],"direct":[89],"way,":[90],"also":[92],"find":[93],"out":[94],"precisely":[95],"which":[96],"choices":[97],"that":[101,115,123],"make":[102],"singular.":[106],"case,":[111],"it":[112],"is":[113,127,140],"shown":[114],"if":[116],"chosen":[121],"such":[122],"scheme":[126,139],"dual":[128],"consistent,":[129],"matrix":[132],"can":[133],"become":[134],"singular":[135],"even":[136],"when":[137],"energy":[141],"stable.":[142],"inverse":[144],"formulas":[145],"hold":[146],"for":[147],"SBP-SAT":[148],"operators":[149],"arbitrary":[151],"order":[152,159],"accuracy.":[154],"For":[155],"fourth":[158],"accurate":[160],"provided":[165],"explicitly.":[166]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}