{"id":"https://openalex.org/W1972300716","doi":"https://doi.org/10.1090/s0025-5718-98-00930-2","title":"Implicit-explicit multistep finite element methods for nonlinear parabolic problems","display_name":"Implicit-explicit multistep finite element methods for nonlinear parabolic problems","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1972300716","doi":"https://doi.org/10.1090/s0025-5718-98-00930-2","mag":"1972300716"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-98-00930-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00930-2","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00930-2/S0025-5718-98-00930-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00930-2/S0025-5718-98-00930-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013053188","display_name":"Georgios Akrivis","orcid":"https://orcid.org/0000-0003-1851-0757"},"institutions":[{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Georgios Akrivis","raw_affiliation_strings":["Department of Computer Science, University of Ioannina, 451 10 Ioannina, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Ioannina, 451 10 Ioannina, Greece","institution_ids":["https://openalex.org/I194019607"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045416083","display_name":"Michel Crouzeix","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Michel Crouzeix","raw_affiliation_strings":["IRMAR, Universit\u00c3\u00a9 de Rennes I, Campus de Beaulieu, F-35042 Rennes, France","IRMAR, Universit\u00e9 de Rennes I, Campus de Beaulieu, F-35042 Rennes, France"],"affiliations":[{"raw_affiliation_string":"IRMAR, Universit\u00c3\u00a9 de Rennes I, Campus de Beaulieu, F-35042 Rennes, France","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I4210161663"]},{"raw_affiliation_string":"IRMAR, Universit\u00e9 de Rennes I, Campus de Beaulieu, F-35042 Rennes, France","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I4210161663"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105693474","display_name":"Charalambos Makridakis","orcid":null},"institutions":[{"id":"https://openalex.org/I142617266","display_name":"University of Crete","ror":"https://ror.org/00dr28g20","country_code":"GR","type":"education","lineage":["https://openalex.org/I142617266"]},{"id":"https://openalex.org/I8901234","display_name":"Foundation for Research and Technology Hellas","ror":"https://ror.org/052rphn09","country_code":"GR","type":"facility","lineage":["https://openalex.org/I8901234"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Charalambos Makridakis","raw_affiliation_strings":["Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece, and IACM, Foundation for Research and Technology - Hellas, 711 10 Heraklion, Crete, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece, and IACM, Foundation for Research and Technology - Hellas, 711 10 Heraklion, Crete, Greece","institution_ids":["https://openalex.org/I8901234","https://openalex.org/I142617266"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013053188"],"corresponding_institution_ids":["https://openalex.org/I194019607"],"apc_list":null,"apc_paid":null,"fwci":1.526,"has_fulltext":true,"cited_by_count":87,"citation_normalized_percentile":{"value":0.81048878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"67","issue":"222","first_page":"457","last_page":"477"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9991999864578247,"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/algorithm","display_name":"Algorithm","score":0.5861189365386963},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.565644383430481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.392768919467926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37431973218917847},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23478546738624573}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5861189365386963},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.565644383430481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.392768919467926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37431973218917847},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23478546738624573}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-98-00930-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00930-2","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00930-2/S0025-5718-98-00930-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.103.9864","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.9864","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.tem.uoc.gr/~makr/ACM1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.145.6851","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.6851","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/1998-67-222/S0025-5718-98-00930-2/S0025-5718-98-00930-2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-98-00930-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00930-2","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00930-2/S0025-5718-98-00930-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322644","display_name":"University of Crete","ror":"https://ror.org/00dr28g20"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1972300716.pdf","grobid_xml":"https://content.openalex.org/works/W1972300716.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W358447554","https://openalex.org/W879521399","https://openalex.org/W1594759473","https://openalex.org/W1600945564","https://openalex.org/W1964896841","https://openalex.org/W1995504856","https://openalex.org/W2032257836","https://openalex.org/W2041001120","https://openalex.org/W2041968314","https://openalex.org/W2049688341","https://openalex.org/W2078767654","https://openalex.org/W2080044677","https://openalex.org/W2082621526","https://openalex.org/W2085122115","https://openalex.org/W2088626621","https://openalex.org/W2090344516","https://openalex.org/W2104410771","https://openalex.org/W2289109300","https://openalex.org/W2586273518","https://openalex.org/W3023894225","https://openalex.org/W4249116854","https://openalex.org/W4291439952","https://openalex.org/W4292366025","https://openalex.org/W4293515545"],"related_works":["https://openalex.org/W2066091055","https://openalex.org/W2040186499","https://openalex.org/W4377003522","https://openalex.org/W2360394982","https://openalex.org/W146891625","https://openalex.org/W2386767533","https://openalex.org/W2061794300","https://openalex.org/W2385374403","https://openalex.org/W2086460959","https://openalex.org/W1993270364"],"abstract_inverted_index":{"We":[0,74],"approximate":[1],"the":[2,34,40,60,67,86,89],"solution":[3,61],"of":[4,33,62,101],"initial":[5],"boundary":[6],"value":[7],"problems":[8],"for":[9,70],"nonlinear":[10],"parabolic":[11],"equations.":[12],"In":[13],"space":[14],"we":[15],"discretize":[16],"by":[17],"finite":[18],"element":[19],"methods.":[20],"The":[21,43,80],"discretization":[22],"in":[23,92,105],"time":[24,58,72],"is":[25,36],"based":[26],"on":[27],"linear":[28,64],"multistep":[29],"schemes.":[30],"One":[31],"part":[32],"equation":[35],"discretized":[37],"implicitly":[38],"and":[39,49,88],"other":[41],"explicitly.":[42],"resulting":[44],"schemes":[45],"are":[46,83],"stable,":[47],"consistent":[48],"very":[50],"efficient,":[51],"since":[52],"their":[53],"implementation":[54],"requires":[55],"at":[56],"each":[57],"step":[59],"a":[63,99],"system":[65],"with":[66],"same":[68],"matrix":[69],"all":[71],"levels.":[73],"derive":[75],"optimal":[76],"order":[77],"error":[78],"estimates.":[79],"abstract":[81],"results":[82],"applied":[84],"to":[85,98],"Kuramoto-Sivashinsky":[87],"Cahn-Hilliard":[90],"equations":[91,104],"one":[93],"dimension,":[94],"as":[95,97],"well":[96],"class":[100],"reaction":[102],"diffusion":[103],"<inline-formula":[106,145],"content-type=\"math/mathml\">":[107,146],"<mml:math":[108,147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[109,148],"alttext=\"double-struck":[110],"upper":[111],"R":[112],"Superscript":[113],"nu":[114],"Baseline":[115],"comma\">":[116],"<mml:semantics>":[117,155],"<mml:mrow>":[118,156],"<mml:msup>":[119],"<mml:mrow":[120,122,128],"class=\"MJX-TeXAtom-ORD\">":[121,123,129],"<mml:mi":[124],"mathvariant=\"double-struck\">R</mml:mi>":[125],"</mml:mrow>":[126,127,133,136,164],"<mml:mi>":[130,157],"\u03bd":[131,158],"</mml:mi>":[132,159],"</mml:msup>":[134],"<mml:mo>,</mml:mo>":[135,162],"<mml:annotation":[137,165],"encoding=\"application/x-tex\">{\\mathbb":[138],"{R}}":[139],"^{\\nu":[140],"},</mml:annotation>":[141],"</mml:semantics>":[142,170],"</mml:math>":[143,171],"</inline-formula>":[144,172],"alttext=\"nu":[149],"equals":[150],"2":[151],"comma":[152],"3":[153],"period\">":[154],"<mml:mo>=</mml:mo>":[160],"<mml:mn>2</mml:mn>":[161],"<mml:mn>3.</mml:mn>":[163],"encoding=\"application/x-tex\">\\nu":[166],"=":[167],"2,":[168],"3.</mml:annotation>":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
