{"id":"https://openalex.org/W3200732442","doi":"https://doi.org/10.1007/s00211-021-01235-2","title":"Numerical analysis of a finite element formulation of the P2D model for Lithium-ion cells","display_name":"Numerical analysis of a finite element formulation of the P2D model for Lithium-ion cells","publication_year":2021,"publication_date":"2021-10-23","ids":{"openalex":"https://openalex.org/W3200732442","doi":"https://doi.org/10.1007/s00211-021-01235-2","mag":"3200732442"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-021-01235-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-021-01235-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-021-01235-2.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/s00211-021-01235-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054172837","display_name":"Rodolfo Bermejo","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120607","display_name":"Light Prescriptions Innovators (Spain)","ror":"https://ror.org/01wekt990","country_code":"ES","type":"company","lineage":["https://openalex.org/I4210120607","https://openalex.org/I4210161798"]},{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"R. Bermejo","raw_affiliation_strings":["Dpto. Matemtica Aplicada a la Ingeniera Industrial, ETSII Universidad Politcnica de Madrid, Madrid, Spain","terio de Ciencia, Innovacin y Universidades of Spain","Technical University of Madrid,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. Matemtica Aplicada a la Ingeniera Industrial, ETSII Universidad Politcnica de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"terio de Ciencia, Innovacin y Universidades of Spain","institution_ids":["https://openalex.org/I4210120607"]},{"raw_affiliation_string":"Technical University of Madrid,","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054172837"],"corresponding_institution_ids":["https://openalex.org/I4210120607","https://openalex.org/I88060688"],"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":0.1328249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"149","issue":"3","first_page":"463","last_page":"505"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10663","display_name":"Advanced Battery Technologies Research","score":0.9733999967575073,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"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/T10663","display_name":"Advanced Battery Technologies Research","score":0.9733999967575073,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T11416","display_name":"Numerical methods for differential equations","score":0.972599983215332,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9664999842643738,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6975632309913635},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6793862581253052},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6307917237281799},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.5063251256942749},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4792335331439972},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4665358364582062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42960673570632935},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.420918732881546},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3220157027244568},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.25374725461006165},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22856402397155762},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07590296864509583}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6975632309913635},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6793862581253052},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6307917237281799},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.5063251256942749},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4792335331439972},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4665358364582062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42960673570632935},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.420918732881546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3220157027244568},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.25374725461006165},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22856402397155762},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07590296864509583},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00211-021-01235-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-021-01235-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-021-01235-2.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2109.10647","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.10647","pdf_url":"https://arxiv.org/pdf/2109.10647","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:3200732442","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2109.10647.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.2109.10647","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2109.10647","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00211-021-01235-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-021-01235-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-021-01235-2.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322138","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3200732442.pdf","grobid_xml":"https://content.openalex.org/works/W3200732442.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1547403762","https://openalex.org/W1674659126","https://openalex.org/W1866311589","https://openalex.org/W1975676156","https://openalex.org/W1976792512","https://openalex.org/W2036620152","https://openalex.org/W2094562977","https://openalex.org/W2113449668","https://openalex.org/W2160737479","https://openalex.org/W2167993255","https://openalex.org/W2339441077","https://openalex.org/W2544547112","https://openalex.org/W2886334531","https://openalex.org/W2950902489","https://openalex.org/W2962868724","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W3005761225","https://openalex.org/W3142306316","https://openalex.org/W2187707214","https://openalex.org/W2807072684","https://openalex.org/W2178791305","https://openalex.org/W2555940299","https://openalex.org/W2053139767","https://openalex.org/W2129425256","https://openalex.org/W2042816276","https://openalex.org/W2386151497","https://openalex.org/W1656605191","https://openalex.org/W2749322924","https://openalex.org/W2094849454","https://openalex.org/W1993061628","https://openalex.org/W2793278651","https://openalex.org/W3140961869","https://openalex.org/W2127990116","https://openalex.org/W2139715454","https://openalex.org/W2082613770","https://openalex.org/W2590645044"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"mathematical":[2],"P2D":[3],"model":[4],"is":[5],"a":[6,30,37],"system":[7],"of":[8,18,29,53,61],"strongly":[9],"coupled":[10],"nonlinear":[11],"parabolic-elliptic":[12],"equations":[13],"that":[14],"describes":[15],"the":[16,26,45,49,57,62],"electrodynamics":[17],"lithium-ion":[19],"batteries.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24],"present":[25],"numerical":[27],"analysis":[28],"finite":[31],"element-implicit":[32],"Euler":[33],"scheme":[34],"for":[35,43],"such":[36],"model.":[38],"We":[39],"obtain":[40],"error":[41],"estimates":[42],"both":[44],"spatially":[46],"semidiscrete":[47],"and":[48,55,59],"fully":[50,63],"discrete":[51,64],"systems":[52],"equations,":[54],"establish":[56],"existence":[58],"uniqueness":[60],"solution.":[65]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
