{"id":"https://openalex.org/W7135205793","doi":"https://doi.org/10.48550/arxiv.2603.11696","title":"Non-uniform $\u03b1$-Robust Alikhanov Mixed FEM with Optimal Convergence for the Time-Fractional Allen--Cahn Equation","display_name":"Non-uniform $\u03b1$-Robust Alikhanov Mixed FEM with Optimal Convergence for the Time-Fractional Allen--Cahn Equation","publication_year":2026,"publication_date":"2026-03-12","ids":{"openalex":"https://openalex.org/W7135205793","doi":"https://doi.org/10.48550/arxiv.2603.11696"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.11696","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11696","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.11696","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011706761","display_name":"Abhinav Jha","orcid":"https://orcid.org/0000-0003-1188-8909"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jha, Abhinav","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071321514","display_name":"Samir Karaa","orcid":"https://orcid.org/0000-0003-4837-0759"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karaa, Samir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007087450","display_name":"Aditi Tomar","orcid":"https://orcid.org/0000-0001-6121-0229"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tomar, Aditi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.6071000099182129,"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"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.6071000099182129,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.3206999897956848,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.009800000116229057,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6617000102996826},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6015999913215637},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5961999893188477},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5742999911308289},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4984000027179718},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47049999237060547},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.39079999923706055},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.3903000056743622}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7827000021934509},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6617000102996826},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6015999913215637},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5986999869346619},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5961999893188477},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5742999911308289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4993000030517578},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4984000027179718},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47049999237060547},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3903000056743622},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2802000045776367},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2770000100135803},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.26179999113082886}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.11696","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11696","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.11696","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11696","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,60],"investigate":[1],"a":[2,12,18,24,68],"mixed":[3],"finite":[4],"element":[5],"method":[6],"for":[7,28,54,71],"the":[8,29,37,48,55,73,76,85,90,93,107],"spatial":[9],"discretization":[10],"of":[11],"time-fractional":[13],"Allen--Cahn":[14],"equation":[15],"defined":[16],"on":[17,36],"convex":[19],"polyhedral":[20],"domain,":[21],"combined":[22],"with":[23,82],"nonuniform":[25],"Alikhanov":[26],"scheme":[27],"temporal":[30],"approximation.":[31],"Under":[32],"suitable":[33],"regularity":[34,52],"assumptions":[35],"initial":[38],"data":[39],"that":[40,92],"are":[41,80,103],"weaker":[42],"than":[43],"those":[44],"typically":[45],"imposed":[46],"in":[47,89],"literature,":[49],"we":[50],"establish":[51],"results":[53],"solution":[56,74],"and":[57,75],"its":[58],"flux.":[59,77],"then":[61],"derive":[62],"optimal":[63],"$L^2$-error":[64],"estimates,":[65],"up":[66],"to":[67,84,105],"logarithmic":[69],"factor,":[70],"both":[72],"The":[78],"estimates":[79],"robust":[81],"respect":[83],"fractional":[86],"order":[87],"$\u03b1$,":[88],"sense":[91],"associated":[94],"constants":[95],"remain":[96],"bounded":[97],"as":[98],"$\u03b1\\to":[99],"1^{-}$.":[100],"Numerical":[101],"experiments":[102],"presented":[104],"confirm":[106],"theoretical":[108],"findings.":[109]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-14T00:00:00"}
