{"id":"https://openalex.org/W4389983992","doi":"https://doi.org/10.48550/arxiv.2312.10860","title":"The interior penalty virtual element method for fourth-order singular perturbation problems","display_name":"The interior penalty virtual element method for fourth-order singular perturbation problems","publication_year":2023,"publication_date":"2023-12-18","ids":{"openalex":"https://openalex.org/W4389983992","doi":"https://doi.org/10.48550/arxiv.2312.10860"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2312.10860","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.10860","pdf_url":"https://arxiv.org/pdf/2312.10860","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2312.10860","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071610696","display_name":"Fang Feng","orcid":"https://orcid.org/0000-0003-2371-2855","observed_orcids":["https://orcid.org/0000-0003-2371-2855"]},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng, Fang","raw_affiliation_strings":["School of Mathematics and Statistics , Nanjing University of Science and Technology , Nanjing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Nanjing University of Science and Technology , Nanjing , China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100397986","display_name":"Yue Yu","orcid":"https://orcid.org/0000-0002-8309-1838","observed_orcids":["https://orcid.org/0000-0002-8309-1838","https://orcid.org/0000-0002-9150-3986","https://orcid.org/0009-0001-0279-7266"]},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu, Yue","raw_affiliation_strings":["School of Mathematics and Computational Science , Hunan Key Laboratory for Computation and Simulation in Science and Engineering , Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education , Xiangtan University , Xiangtan , Hunan 411105 , PR China","School of Mathematics and Statistics , Nanjing University of Science and Technology , Nanjing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science , Hunan Key Laboratory for Computation and Simulation in Science and Engineering , Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education , Xiangtan University , Xiangtan , Hunan 411105 , PR China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"School of Mathematics and Statistics , Nanjing University of Science and Technology , Nanjing , China","institution_ids":["https://openalex.org/I36399199"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.8744999766349792,"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":0.8744999766349792,"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":0.12349999696016312,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.00019999999494757503,"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/penalty-parameter-selection","display_name":"penalty parameter selection","score":0.8569999933242798},{"id":"https://openalex.org/keywords/optimal-convergence","display_name":"optimal convergence","score":0.7279999852180481},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"uniform convergence","score":0.9380000233650208},{"id":"https://openalex.org/keywords/energy-norm-error-estimates","display_name":"energy norm error estimates","score":0.703000009059906},{"id":"https://openalex.org/keywords/bilinear-forms","display_name":"bilinear forms","score":0.5040000081062317}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6176409721374512},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.6167014241218567},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.5867175459861755},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5842243432998657},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.562450647354126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5165659189224243},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5088708400726318},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44786304235458374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4431946575641632},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.41670554876327515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4024992287158966},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34977519512176514},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08976417779922485},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08913370966911316},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0791986882686615},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2312.10860","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.10860","pdf_url":"https://arxiv.org/pdf/2312.10860","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2312.10860","doi":"https://doi.org/10.48550/arxiv.2312.10860","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2312.10860","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2312.10860","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.10860","pdf_url":"https://arxiv.org/pdf/2312.10860","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5400000214576721}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389983992.pdf","grobid_xml":"https://content.openalex.org/works/W4389983992.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4327639758","https://openalex.org/W4200053212","https://openalex.org/W2116787190","https://openalex.org/W2235548299","https://openalex.org/W2197675418","https://openalex.org/W2154304710","https://openalex.org/W4220877270","https://openalex.org/W2019676381","https://openalex.org/W1963546854","https://openalex.org/W3129644063"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"dedicated":[3],"to":[4,29,65],"the":[5,15,30,35,47,53,61,67,71,82,94,98],"numerical":[6],"solution":[7],"of":[8,46,70,90],"a":[9,87],"fourth-order":[10],"singular":[11],"perturbation":[12,95],"problem":[13],"using":[14],"interior":[16],"penalty":[17,36,48],"virtual":[18],"element":[19,57],"method":[20],"(IPVEM)":[21],"proposed":[22],"in":[23,34,81,97],"[42].":[24],"The":[25],"study":[26],"introduces":[27],"modifications":[28],"jumps":[31],"and":[32,85],"averages":[33],"term,":[37],"as":[38,40],"well":[39],"presents":[41],"an":[42],"automated":[43],"mesh-dependent":[44],"selection":[45],"parameter.":[49],"Drawing":[50],"inspiration":[51],"from":[52],"modified":[54],"Morley":[55],"finite":[56],"methods,":[58],"we":[59,77],"leverage":[60],"conforming":[62],"interpolation":[63],"technique":[64],"handle":[66],"lower":[68],"part":[69],"bilinear":[72],"form.":[73],"Through":[74],"our":[75],"analysis,":[76],"establish":[78],"optimal":[79],"convergence":[80,92],"energy":[83],"norm":[84],"provide":[86],"rigorous":[88],"proof":[89],"uniform":[91],"concerning":[93],"parameter":[96],"lowest-order":[99],"case.":[100]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-10-13T10:08:12.033832","created_date":"2023-12-20T00:00:00"}
