{"id":"https://openalex.org/W2521195550","doi":"https://doi.org/10.1007/s00211-018-0949-3","title":"Data assimilation for the heat equation using stabilized finite element methods","display_name":"Data assimilation for the heat equation using stabilized finite element methods","publication_year":2018,"publication_date":"2018-02-10","ids":{"openalex":"https://openalex.org/W2521195550","doi":"https://doi.org/10.1007/s00211-018-0949-3","mag":"2521195550","pmid":"https://pubmed.ncbi.nlm.nih.gov/29973740"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-018-0949-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-018-0949-3","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-018-0949-3.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-018-0949-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011409848","display_name":"Erik Burman","orcid":"https://orcid.org/0000-0003-4287-7241"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Erik Burman","raw_affiliation_strings":["Department of Mathematics, University College London, Gower Street, London, WC1E 6BT UK","Department of Mathematics,University College London, Gower Street, London WC1E 6BT, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College London, Gower Street, London, WC1E 6BT UK","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"Department of Mathematics,University College London, Gower Street, London WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044437642","display_name":"Lauri Oksanen","orcid":"https://orcid.org/0000-0002-3228-7507"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lauri Oksanen","raw_affiliation_strings":["Department of Mathematics, University College London, Gower Street, London, WC1E 6BT UK","Department of Mathematics, University College, London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College London, Gower Street, London, WC1E 6BT UK","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"Department of Mathematics, University College, London, London, UK","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0,"citation_normalized_percentile":{"value":0.02584887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"139","issue":"3","first_page":"505","last_page":"528"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9983999729156494,"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":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8426926136016846},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7055792212486267},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.6494266390800476},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6139488220214844},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.5984911918640137},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5779881477355957},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5725183486938477},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.562576174736023},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.47631654143333435},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3645787239074707},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34939810633659363},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31714367866516113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3105212450027466},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06643298268318176}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8426926136016846},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7055792212486267},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.6494266390800476},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6139488220214844},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5984911918640137},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5779881477355957},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5725183486938477},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.562576174736023},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.47631654143333435},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3645787239074707},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34939810633659363},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31714367866516113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3105212450027466},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06643298268318176},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s00211-018-0949-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-018-0949-3","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-018-0949-3.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmid:29973740","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29973740","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische mathematik","raw_type":null},{"id":"pmh:oai:arXiv.org:1609.05107","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1609.05107","pdf_url":"https://arxiv.org/pdf/1609.05107","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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:2521195550","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1609.05107.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":"pmh:oai:eprints.ucl.ac.uk.OAI2:1518356","is_oa":false,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/1518356/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   Numerische Mathematik       (2018)     (In press).  ","raw_type":"Article"},{"id":"pmh:oai:europepmc.org:4977934","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6004001","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"doi:10.48550/arxiv.1609.05107","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1609.05107","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/s00211-018-0949-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-018-0949-3","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-018-0949-3.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1215260848","display_name":null,"funder_award_id":"EP/J002313/2","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1982737232","display_name":null,"funder_award_id":"EP/P01576X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5351140740","display_name":"The inverse source problem arising in Photoacoustic Tomography","funder_award_id":"EP/L026473/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7743258531","display_name":null,"funder_award_id":"EP/J002313/2","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G797993351","display_name":"Geometrically unfitted finite element methods for inverse identification of geometries and shape optimization","funder_award_id":"EP/P01576X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8863664214","display_name":null,"funder_award_id":"EP/L026473/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320286","display_name":"University College London","ror":"https://ror.org/02jx3x895"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2521195550.pdf","grobid_xml":"https://content.openalex.org/works/W2521195550.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1509474121","https://openalex.org/W1570089119","https://openalex.org/W1601728065","https://openalex.org/W1979771104","https://openalex.org/W1986978892","https://openalex.org/W1996629590","https://openalex.org/W2004259617","https://openalex.org/W2009985306","https://openalex.org/W2027753843","https://openalex.org/W2031838089","https://openalex.org/W2042669370","https://openalex.org/W2044305135","https://openalex.org/W2050687116","https://openalex.org/W2057187260","https://openalex.org/W2067354736","https://openalex.org/W2069129680","https://openalex.org/W2078031695","https://openalex.org/W2094254426","https://openalex.org/W2149846618","https://openalex.org/W2156526309","https://openalex.org/W2521794430","https://openalex.org/W2527369378","https://openalex.org/W2963141323","https://openalex.org/W3204708751","https://openalex.org/W4205783823","https://openalex.org/W4248122039"],"related_works":["https://openalex.org/W2993328524","https://openalex.org/W2759510049","https://openalex.org/W3142724817","https://openalex.org/W2929902583","https://openalex.org/W2061682845","https://openalex.org/W2373717889","https://openalex.org/W2810001934","https://openalex.org/W2098982515","https://openalex.org/W3084277542","https://openalex.org/W2984720486","https://openalex.org/W2808511068","https://openalex.org/W2944989483","https://openalex.org/W2528740671","https://openalex.org/W2791004907","https://openalex.org/W2059078700","https://openalex.org/W2081212810","https://openalex.org/W2045340965","https://openalex.org/W2951235447","https://openalex.org/W2767598523","https://openalex.org/W2945374908"],"abstract_inverted_index":{"We":[0],"consider":[1],"data":[2,92],"assimilation":[3,93],"for":[4,114],"the":[5,20,31,52,56,64,75,79,84,87,103,115,121],"heat":[6],"equation":[7],"using":[8],"a":[9,45],"finite":[10,35,80],"element":[11,81],"space":[12,38,82],"semi-discretization.":[13],"The":[14,37],"approach":[15],"is":[16,41,125],"optimization":[17],"based,":[18],"but":[19],"design":[21],"of":[22,33,51,55,63,78,86],"regularization":[23],"operators":[24],"and":[25,59,83],"parameters":[26],"rely":[27],"on":[28,107],"techniques":[29],"from":[30],"theory":[32],"stabilized":[34],"elements.":[36],"semi-discretized":[39],"system":[40],"shown":[42],"to":[43,101,109,118],"admit":[44],"unique":[46],"solution.":[47],"Combining":[48],"sharp":[49],"estimates":[50,62,72,113],"numerical":[53,122],"stability":[54,61,85,97,112],"discrete":[57],"scheme":[58],"conditional":[60],"ill-posed":[65],"continuous":[66,88,116],"pde-model":[67],"we":[68],"then":[69],"derive":[70],"error":[71],"that":[73],"reflect":[74],"approximation":[76],"order":[77],"model.":[89],"Two":[90],"different":[91,96],"situations":[94],"with":[95,120],"properties":[98],"are":[99],"considered":[100],"illustrate":[102],"framework.":[104],"Full":[105],"detail":[106],"how":[108],"adapt":[110],"known":[111],"model":[117],"work":[119],"analysis":[123],"framework":[124],"given":[126],"in":[127],"\"Appendix\".":[128]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
