{"id":"https://openalex.org/W2141657895","doi":"https://doi.org/10.2478/cmam-2010-0013","title":"A Flux-Corrected Finite Element Method for Chemotaxis Problems","display_name":"A Flux-Corrected Finite Element Method for Chemotaxis Problems","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2141657895","doi":"https://doi.org/10.2478/cmam-2010-0013","mag":"2141657895"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2010-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0013","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0013/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0013/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035238589","display_name":"Robert Strehl","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"R. Strehl","raw_affiliation_strings":["1Institute of Applied Mathematics, LS III, TU Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"1Institute of Applied Mathematics, LS III, TU Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042162342","display_name":"A. Yu. Sokolov","orcid":"https://orcid.org/0000-0002-2866-2706"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"A. Sokolov","raw_affiliation_strings":["1Institute of Applied Mathematics, LS III, TU Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"1Institute of Applied Mathematics, LS III, TU Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090390734","display_name":"Dmitri Kuzmin","orcid":"https://orcid.org/0000-0003-0084-9752"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"D. Kuzmin","raw_affiliation_strings":["1Institute of Applied Mathematics, LS III, TU Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"1Institute of Applied Mathematics, LS III, TU Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059837563","display_name":"Stefan Turek","orcid":"https://orcid.org/0000-0002-9740-6087"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S. Turek","raw_affiliation_strings":["1Institute of Applied Mathematics, LS III, TU Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"1Institute of Applied Mathematics, LS III, TU Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035238589"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":null,"apc_paid":null,"fwci":1.8856,"has_fulltext":true,"cited_by_count":44,"citation_normalized_percentile":{"value":0.84594257,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"10","issue":"2","first_page":"219","last_page":"232"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"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":1.0,"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/T10336","display_name":"Cancer Cells and Metastasis","score":0.9783999919891357,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chemotaxis","display_name":"Chemotaxis","score":0.7676866054534912},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7505968809127808},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7280194759368896},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6313821077346802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5706267356872559},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.561744749546051},{"id":"https://openalex.org/keywords/flux","display_name":"Flux (metallurgy)","score":0.5528513789176941},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5366769433021545},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4767495095729828},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46348267793655396},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4226859211921692},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2648061513900757},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14056971669197083},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.06255078315734863},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06059667468070984},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.05324855446815491}],"concepts":[{"id":"https://openalex.org/C54166955","wikidata":"https://www.wikidata.org/wiki/Q658145","display_name":"Chemotaxis","level":3,"score":0.7676866054534912},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7505968809127808},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7280194759368896},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6313821077346802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5706267356872559},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.561744749546051},{"id":"https://openalex.org/C68709404","wikidata":"https://www.wikidata.org/wiki/Q1134475","display_name":"Flux (metallurgy)","level":2,"score":0.5528513789176941},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5366769433021545},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4767495095729828},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46348267793655396},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4226859211921692},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2648061513900757},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14056971669197083},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.06255078315734863},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06059667468070984},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.05324855446815491},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0},{"id":"https://openalex.org/C170493617","wikidata":"https://www.wikidata.org/wiki/Q208467","display_name":"Receptor","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/cmam-2010-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0013","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0013/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.705.486","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.705.486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathematik.tu-dortmund.de/lsiii/cms/papers/StrehlSokolovKuzminTurek2009.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.2478/cmam-2010-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0013","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0013/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.6899999976158142,"display_name":"Life in Land"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2141657895.pdf","grobid_xml":"https://content.openalex.org/works/W2141657895.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W127537615","https://openalex.org/W625415786","https://openalex.org/W1515194959","https://openalex.org/W1660301190","https://openalex.org/W1841343875","https://openalex.org/W1965214685","https://openalex.org/W1973224983","https://openalex.org/W1977005850","https://openalex.org/W1987221447","https://openalex.org/W1987347396","https://openalex.org/W1987971235","https://openalex.org/W1996819678","https://openalex.org/W2007565412","https://openalex.org/W2021117151","https://openalex.org/W2033483553","https://openalex.org/W2042892258","https://openalex.org/W2052607781","https://openalex.org/W2062598371","https://openalex.org/W2068213416","https://openalex.org/W2074203477","https://openalex.org/W2078234004","https://openalex.org/W2086412476","https://openalex.org/W2105387413","https://openalex.org/W2126617016","https://openalex.org/W2150010560","https://openalex.org/W2154582065","https://openalex.org/W2162288469","https://openalex.org/W2165967192","https://openalex.org/W2168977801","https://openalex.org/W2749486094","https://openalex.org/W4205351140","https://openalex.org/W6603039838","https://openalex.org/W6603228137"],"related_works":["https://openalex.org/W1596865785","https://openalex.org/W2085357479","https://openalex.org/W2417007386","https://openalex.org/W1993973863","https://openalex.org/W2055696851","https://openalex.org/W2324487000","https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"implicit":[2],"flux-corrected":[3],"transport":[4],"(FCT)":[5],"algorithm":[6],"has":[7,24,64],"been":[8,25,66],"developed":[9],"for":[10,56,71],"a":[11,29,57],"class":[12],"of":[13,18,45],"chemotaxis":[14,59,75],"models.":[15],"The":[16,42],"coefficients":[17],"the":[19,38,46,53,69,82,87],"Galerkin":[20],"finite":[21],"element":[22],"discretization":[23],"adjusted":[26],"in":[27,78,86],"such":[28],"way":[30],"as":[31],"to":[32],"guarantee":[33],"mass":[34],"conservation":[35],"and":[36],"keep":[37],"cell":[39],"density":[40],"nonnegative.":[41],"numerical":[43],"behaviour":[44],"proposed":[47],"highresolution":[48],"scheme":[49],"is":[50],"tested":[51],"on":[52],"blow-up":[54],"problem":[55],"minimal":[58],"model":[60,76],"with":[61,81],"singularities.":[62],"It":[63],"also":[65],"shown":[67],"that":[68],"results":[70],"an":[72],"Escherichia":[73],"coli":[74],"are":[77],"good":[79],"agreement":[80],"experimental":[83],"data":[84],"reported":[85],"literature.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}