{"id":"https://openalex.org/W4283374988","doi":"https://doi.org/10.1515/jnma-2021-0113","title":"Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder","display_name":"Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder","publication_year":2022,"publication_date":"2022-06-24","ids":{"openalex":"https://openalex.org/W4283374988","doi":"https://doi.org/10.1515/jnma-2021-0113"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2021-0113","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2021-0113","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014361031","display_name":"Monika Bal\u00e1zsov\u00e1","orcid":"https://orcid.org/0000-0002-4654-421X"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Monika Bal\u00e1zsov\u00e1","raw_affiliation_strings":["Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering , Prague , Czech Republic"],"affiliations":[{"raw_affiliation_string":"Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering , Prague , Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015816042","display_name":"Miloslav Feistauer","orcid":"https://orcid.org/0000-0003-1815-721X"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Miloslav Feistauer","raw_affiliation_strings":["Charles University, Faculty of Mathematics and Physics , Prague , Czech Republic"],"affiliations":[{"raw_affiliation_string":"Charles University, Faculty of Mathematics and Physics , Prague , Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113777673","display_name":"Anna\u2010Margarete S\u00e4ndig","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Anna-Margarete S\u00e4ndig","raw_affiliation_strings":["Universit\u00e4t Stuttgart, IANS , Stuttgart , Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Stuttgart, IANS , Stuttgart , Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014361031"],"corresponding_institution_ids":["https://openalex.org/I44504214"],"apc_list":null,"apc_paid":null,"fwci":0.1626,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.39777044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"0","issue":"0","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9987000226974487,"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/T10514","display_name":"Numerical methods in engineering","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.8889880180358887},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6581062078475952},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6568238139152527},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6456925868988037},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6332924365997314},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6214771866798401},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6090987324714661},{"id":"https://openalex.org/keywords/cylinder","display_name":"Cylinder","score":0.5429880023002625},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.517634928226471},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.49862051010131836},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46614447236061096},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4109984338283539},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24272620677947998},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.20077183842658997}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8889880180358887},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6581062078475952},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6568238139152527},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6456925868988037},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6332924365997314},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6214771866798401},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6090987324714661},{"id":"https://openalex.org/C203311528","wikidata":"https://www.wikidata.org/wiki/Q34132","display_name":"Cylinder","level":2,"score":0.5429880023002625},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.517634928226471},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.49862051010131836},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46614447236061096},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4109984338283539},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24272620677947998},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.20077183842658997},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/jnma-2021-0113","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2021-0113","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1972186223","https://openalex.org/W2002074992","https://openalex.org/W2002482484","https://openalex.org/W2011538814","https://openalex.org/W2027310686","https://openalex.org/W2054154406","https://openalex.org/W2058567087","https://openalex.org/W2065001119","https://openalex.org/W2070798173","https://openalex.org/W2102944072","https://openalex.org/W2110377803","https://openalex.org/W2136033233","https://openalex.org/W2406976758","https://openalex.org/W2794725725","https://openalex.org/W4235661189","https://openalex.org/W4247821411","https://openalex.org/W4256055182"],"related_works":["https://openalex.org/W4232993046","https://openalex.org/W2019543145","https://openalex.org/W1988761177","https://openalex.org/W2058549403","https://openalex.org/W3036336759","https://openalex.org/W2168805210","https://openalex.org/W2043686470","https://openalex.org/W3108492333","https://openalex.org/W3132099539","https://openalex.org/W2078359189"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"note":[3],"we":[4,36],"consider":[5],"a":[6,11,24],"parabolic":[7],"evolution":[8],"equation":[9],"in":[10,44,47,53,88,93],"polygonal":[12],"space-time":[13,79],"cylinder.":[14],"We":[15,104],"show,":[16],"that":[17,86],"the":[18,39,61,65,69,75,78,100,107,111],"elliptic":[19],"part":[20,59],"is":[21,72],"given":[22],"by":[23],"m-accretive":[25],"mapping":[26],"from":[27],"L":[28,32],"q":[29,33],"(\u03a9)":[30],"\u2192":[31],"(\u03a9).":[34],"Therefore":[35],"can":[37],"apply":[38],"theory":[40],"of":[41,60,68,77,99,110],"nonlinear":[42],"semigroups":[43],"Banach":[45],"spaces":[46],"order":[48],"to":[49,74,106],"get":[50],"regularity":[51],"results":[52],"time":[54,94],"and":[55],"space.":[56],"The":[57],"second":[58],"paper":[62],"deals":[63],"with":[64],"numerical":[66],"solution":[67,101],"problem.":[70],"It":[71,84],"dedicated":[73],"application":[76],"discontinuous":[80,95],"Galerkin":[81],"method":[82],"(STDGM).":[83],"means":[85],"both":[87],"space":[89],"as":[90,92],"well":[91],"piecewise":[96],"polynomial":[97],"approximations":[98],"are":[102],"used.":[103],"concentrate":[105],"theoretical":[108],"analysis":[109],"error":[112],"estimation.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}