{"id":"https://openalex.org/W2087631730","doi":"https://doi.org/10.2478/cmam-2010-0025","title":"On Positivity and Maximum-Norm Contractivity in Time Stepping Methods for Parabolic Equations","display_name":"On Positivity and Maximum-Norm Contractivity in Time Stepping Methods for Parabolic Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2087631730","doi":"https://doi.org/10.2478/cmam-2010-0025","mag":"2087631730"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2010-0025","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0025","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0025/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-2010-0025/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052440884","display_name":"A. H. Schatz","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A.H. Schatz","raw_affiliation_strings":["1Department of Mathematics, Cornell University, Ithaca N.Y. 14853, USA"],"affiliations":[{"raw_affiliation_string":"1Department of Mathematics, Cornell University, Ithaca N.Y. 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072856113","display_name":"Vidar Thom\u00e9e","orcid":null},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"V. Thom\u00e8e","raw_affiliation_strings":["2Department of Mathematical Sciences, Chalmers University of Technology, S-41296 G\u00f6teborg, Sweden"],"affiliations":[{"raw_affiliation_string":"2Department of Mathematical Sciences, Chalmers University of Technology, S-41296 G\u00f6teborg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108406032","display_name":"Lars B. Wahlbin","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L.B. Wahlbin","raw_affiliation_strings":["1Department of Mathematics, Cornell University, Ithaca N.Y. 14853, USA"],"affiliations":[{"raw_affiliation_string":"1Department of Mathematics, Cornell University, Ithaca N.Y. 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052440884"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.17647059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"10","issue":"4","first_page":"421","last_page":"443"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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":0.9977999925613403,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9927999973297119,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8261532783508301},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7121909260749817},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.621311604976654},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6197437047958374},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.5871577858924866},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5858915448188782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5608928203582764},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.48991578817367554},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4448186457157135},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43138909339904785},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4219958484172821},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4157698452472687},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.4112517237663269},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.4110139012336731},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2171875238418579},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13639330863952637},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.12803220748901367}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8261532783508301},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7121909260749817},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.621311604976654},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6197437047958374},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.5871577858924866},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5858915448188782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5608928203582764},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.48991578817367554},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4448186457157135},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43138909339904785},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4219958484172821},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4157698452472687},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.4112517237663269},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.4110139012336731},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2171875238418579},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13639330863952637},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.12803220748901367},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/cmam-2010-0025","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0025","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0025/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:publications.lib.chalmers.se:155436","is_oa":false,"landing_page_url":"http://publications.lib.chalmers.se/publication/155436-on-positivity-and-maximum-norm-contractivity-in-time-stepping-methods-for-parabolic-equations","pdf_url":null,"source":{"id":"https://openalex.org/S4377196470","display_name":"Chalmers Publication Library (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text.Article.Journal.PeerReviewed"},{"id":"pmh:oai:research.chalmers.se:155436","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/155436","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.2478/cmam-2010-0025","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0025","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0025/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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2087631730.pdf","grobid_xml":"https://content.openalex.org/works/W2087631730.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1527296550","https://openalex.org/W1983788725","https://openalex.org/W1992477646","https://openalex.org/W2082621526","https://openalex.org/W2142641722","https://openalex.org/W4230941884","https://openalex.org/W6601932915"],"related_works":["https://openalex.org/W2335200596","https://openalex.org/W1991867815","https://openalex.org/W2133369474","https://openalex.org/W2377834777","https://openalex.org/W2524024922","https://openalex.org/W4386556238","https://openalex.org/W3149408653","https://openalex.org/W4390271665","https://openalex.org/W2899284167","https://openalex.org/W1967203400"],"abstract_inverted_index":{"Abstract":[0],"In":[1,68],"an":[2],"earlier":[3],"paper":[4,70],"the":[5,18,25,28,32,36,45,53,61,73,93,103,112,115],"last":[6],"two":[7],"authors":[8],"studied":[9],"spatially":[10],"semidiscrete":[11],"piecewise":[12],"linear":[13],"finite":[14],"element":[15],"approximations":[16],"of":[17,27,35,65],"heat":[19],"equation":[20],"and":[21,114],"showed":[22],"that,":[23],"in":[24,44,84,110,120],"case":[26],"standard":[29],"Galerkin":[30],"method,":[31,98],"solution":[33],"operator":[34],"initial-value":[37],"problem":[38],"is":[39],"neither":[40],"positive":[41],"nor":[42],"contractive":[43],"maximum-norm":[46],"for":[47,52,100],"small":[48],"time,":[49],"but":[50,99],"that":[51],"lumped":[54],"mass":[55],"method":[56],"these":[57],"properties":[58,88],"hold,":[59],"if":[60],"triangulations":[62],"are":[63,105],"essentially":[64],"Delaunay":[66],"type.":[67],"this":[69],"we":[71],"continue":[72],"study":[74],"by":[75,81],"considering":[76],"fully":[77],"discrete":[78],"analogues":[79],"obtained":[80],"discretization":[82],"also":[83],"time.":[85],"The":[86],"above":[87],"then":[89],"carry":[90],"over":[91],"to":[92],"backward":[94],"Euler":[95],"time":[96],"stepping":[97],"other":[101],"methods":[102],"results":[104],"more":[106],"restrictive.":[107],"We":[108],"discuss":[109],"particular":[111],"\u03b8-method":[113],"(0;":[116],"2)":[117],"Pad\u00e9":[118],"approximation":[119],"one":[121],"space":[122],"dimension.":[123]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}