{"id":"https://openalex.org/W3191527521","doi":"https://doi.org/10.1515/jnma-2021-0094","title":"Numerical analysis for a Cahn\u2013Hilliard system modelling tumour growth with chemotaxis and active transport","display_name":"Numerical analysis for a Cahn\u2013Hilliard system modelling tumour growth with chemotaxis and active transport","publication_year":2022,"publication_date":"2022-05-04","ids":{"openalex":"https://openalex.org/W3191527521","doi":"https://doi.org/10.1515/jnma-2021-0094","mag":"3191527521"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2021-0094","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2021-0094","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2108.01507","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071758656","display_name":"Harald Garcke","orcid":"https://orcid.org/0000-0001-5235-2073"},"institutions":[{"id":"https://openalex.org/I60668342","display_name":"University of Regensburg","ror":"https://ror.org/01eezs655","country_code":"DE","type":"education","lineage":["https://openalex.org/I60668342"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Harald Garcke","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Regensburg , 93053 , Regensburg , Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Regensburg , 93053 , Regensburg , Germany","institution_ids":["https://openalex.org/I60668342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042510159","display_name":"Dennis Trautwein","orcid":"https://orcid.org/0009-0000-5136-4566"},"institutions":[{"id":"https://openalex.org/I60668342","display_name":"University of Regensburg","ror":"https://ror.org/01eezs655","country_code":"DE","type":"education","lineage":["https://openalex.org/I60668342"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dennis Trautwein","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Regensburg , 93053 , Regensburg , Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Regensburg , 93053 , Regensburg , Germany","institution_ids":["https://openalex.org/I60668342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042510159"],"corresponding_institution_ids":["https://openalex.org/I60668342"],"apc_list":null,"apc_paid":null,"fwci":1.7813,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.82927632,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"295","last_page":"324"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9940999746322632,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9465000033378601,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chemotaxis","display_name":"Chemotaxis","score":0.7162865996360779},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5099450349807739},{"id":"https://openalex.org/keywords/cahn\u2013hilliard-equation","display_name":"Cahn\u2013Hilliard equation","score":0.4626205265522003},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35880228877067566},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20954552292823792},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.1943119466304779},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.09807544946670532},{"id":"https://openalex.org/keywords/biochemistry","display_name":"Biochemistry","score":0.0804910659790039}],"concepts":[{"id":"https://openalex.org/C54166955","wikidata":"https://www.wikidata.org/wiki/Q658145","display_name":"Chemotaxis","level":3,"score":0.7162865996360779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5099450349807739},{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.4626205265522003},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35880228877067566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20954552292823792},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.1943119466304779},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.09807544946670532},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0804910659790039},{"id":"https://openalex.org/C170493617","wikidata":"https://www.wikidata.org/wiki/Q208467","display_name":"Receptor","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/jnma-2021-0094","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2021-0094","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2108.01507","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.01507","pdf_url":"https://arxiv.org/pdf/2108.01507","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":"pmh:oai:epub.uni-regensburg.de:56965","is_oa":false,"landing_page_url":"https://epub.uni-regensburg.de/56965/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401229","display_name":"University of Regensburg Publication Server (University of Regensburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60668342","host_organization_name":"University of Regensburg","host_organization_lineage":["https://openalex.org/I60668342"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2108.01507","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.01507","pdf_url":"https://arxiv.org/pdf/2108.01507","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W251810509","https://openalex.org/W1494982173","https://openalex.org/W1512153219","https://openalex.org/W1521182415","https://openalex.org/W1605821011","https://openalex.org/W1975968248","https://openalex.org/W1987347396","https://openalex.org/W1998903284","https://openalex.org/W2003173073","https://openalex.org/W2030126035","https://openalex.org/W2039254108","https://openalex.org/W2042669961","https://openalex.org/W2049208793","https://openalex.org/W2052607781","https://openalex.org/W2060052509","https://openalex.org/W2062815311","https://openalex.org/W2067036250","https://openalex.org/W2071643566","https://openalex.org/W2071867803","https://openalex.org/W2073078790","https://openalex.org/W2076868976","https://openalex.org/W2077313431","https://openalex.org/W2088130948","https://openalex.org/W2102952103","https://openalex.org/W2104010300","https://openalex.org/W2105387413","https://openalex.org/W2111564493","https://openalex.org/W2126617016","https://openalex.org/W2138026128","https://openalex.org/W2147156709","https://openalex.org/W2147212734","https://openalex.org/W2160509269","https://openalex.org/W2199169705","https://openalex.org/W2292972364","https://openalex.org/W2394139940","https://openalex.org/W2493549790","https://openalex.org/W2514563839","https://openalex.org/W2581758183","https://openalex.org/W2594425100","https://openalex.org/W2614477650","https://openalex.org/W2619153979","https://openalex.org/W2621583330","https://openalex.org/W2750972839","https://openalex.org/W2912075042","https://openalex.org/W2934526567","https://openalex.org/W2962777676","https://openalex.org/W2963424183","https://openalex.org/W2963683463","https://openalex.org/W2963768558","https://openalex.org/W2992451487","https://openalex.org/W2995727281","https://openalex.org/W3011798359","https://openalex.org/W3021722416","https://openalex.org/W3086809302","https://openalex.org/W3098986732","https://openalex.org/W3104199352","https://openalex.org/W3112647857","https://openalex.org/W3139505501","https://openalex.org/W3159081963","https://openalex.org/W3196290810","https://openalex.org/W4205634890","https://openalex.org/W4234794606","https://openalex.org/W4245654886","https://openalex.org/W4246528370","https://openalex.org/W4253741862"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1596865785","https://openalex.org/W2085357479","https://openalex.org/W2417007386","https://openalex.org/W1993973863","https://openalex.org/W2388783242","https://openalex.org/W1135436615","https://openalex.org/W2975251372","https://openalex.org/W2313472050","https://openalex.org/W2147110523"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"diffuse":[2],"interface":[3],"model":[4,52],"for":[5,32,40,57],"tumour":[6,17,34],"growth":[7],"in":[8,83,116,125],"the":[9,16,33,41,51,58,72,81,84,96],"presence":[10],"of":[11,22,25,50],"a":[12,26,37,45,91],"nutrient":[13],"consumed":[14],"by":[15],"is":[18,104],"considered.":[19],"The":[20],"system":[21],"equations":[23],"consists":[24],"Cahn\u2013Hilliard":[27],"equation":[28,39],"with":[29],"source":[30],"terms":[31],"cells":[35],"and":[36,53,68,74,87,120,127],"reaction\u2013diffusion":[38],"nutrient.":[42],"We":[43,77],"introduce":[44],"fully-discrete":[46],"finite":[47],"element":[48],"approximation":[49],"prove":[54,88],"stability":[55],"bounds":[56],"discrete":[59,65],"scheme.":[60],"Moreover,":[61],"we":[62,107],"show":[63],"that":[64],"solutions":[66],"exist":[67],"depend":[69],"continuously":[70],"on":[71],"initial":[73],"boundary":[75],"data.":[76],"then":[78],"pass":[79],"to":[80,90,95],"limit":[82],"discretization":[85],"parameters":[86],"convergence":[89],"global-in-time":[92],"weak":[93,102],"solution":[94,103],"model.":[97],"Under":[98],"additional":[99],"assumptions,":[100],"this":[101],"unique.":[105],"Finally,":[106],"present":[108],"some":[109,121],"numerical":[110,113],"results":[111],"including":[112],"error":[114],"investigation":[115],"one":[117],"spatial":[118,129],"dimension":[119],"long":[122],"time":[123],"simulations":[124],"two":[126],"three":[128],"dimensions.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
