{"id":"https://openalex.org/W4386745706","doi":"https://doi.org/10.1137/22m1506468","title":"\\({\\boldsymbol{H^1}}\\) -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation","display_name":"\\({\\boldsymbol{H^1}}\\) -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation","publication_year":2023,"publication_date":"2023-09-14","ids":{"openalex":"https://openalex.org/W4386745706","doi":"https://doi.org/10.1137/22m1506468"},"language":"en","primary_location":{"id":"doi:10.1137/22m1506468","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1506468","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5085215169","display_name":"Chaoyu Quan","orcid":"https://orcid.org/0000-0003-3246-8989"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chaoyu Quan","raw_affiliation_strings":["School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, 518172, Guangdong, People\u2019s Republic of China; SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People\u2019s Republic of China","SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0003-3246-8989","affiliations":[{"raw_affiliation_string":"School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, 518172, Guangdong, People\u2019s Republic of China; SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I3045169105","https://openalex.org/I4210116924"]},{"raw_affiliation_string":"SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People's Republic of China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059206683","display_name":"Xu Wu","orcid":"https://orcid.org/0000-0003-0566-4466"},"institutions":[{"id":"https://openalex.org/I100188998","display_name":"Harbin University of Science and Technology","ror":"https://ror.org/04e6y1282","country_code":"CN","type":"education","lineage":["https://openalex.org/I100188998"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Wu","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People\u2019s Republic of China; Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0003-0566-4466","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People\u2019s Republic of China; Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I3045169105","https://openalex.org/I204983213","https://openalex.org/I100188998"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085215169"],"corresponding_institution_ids":["https://openalex.org/I3045169105","https://openalex.org/I4210116924"],"apc_list":null,"apc_paid":null,"fwci":4.0961,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.94583271,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"61","issue":"5","first_page":"2106","last_page":"2132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/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/T10514","display_name":"Numerical methods in engineering","score":0.9976000189781189,"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":0.8145121335983276},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.7280281782150269},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.7079805135726929},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.42626702785491943},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4142098128795624},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4037342071533203},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33479732275009155},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1539098024368286}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8145121335983276},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.7280281782150269},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.7079805135726929},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.42626702785491943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4142098128795624},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4037342071533203},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33479732275009155},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1539098024368286},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1506468","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1506468","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41999998688697815}],"awards":[{"id":"https://openalex.org/G4131480760","display_name":null,"funder_award_id":"12271241","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W110340196","https://openalex.org/W1969312973","https://openalex.org/W2056829543","https://openalex.org/W2062266804","https://openalex.org/W2065232540","https://openalex.org/W2111271983","https://openalex.org/W2165076033","https://openalex.org/W2274070693","https://openalex.org/W2511264644","https://openalex.org/W2601627861","https://openalex.org/W2608656286","https://openalex.org/W2794616828","https://openalex.org/W2799821673","https://openalex.org/W2898636786","https://openalex.org/W2963392111","https://openalex.org/W2971718279","https://openalex.org/W2977085725","https://openalex.org/W3016396690","https://openalex.org/W3016623442","https://openalex.org/W3018009055","https://openalex.org/W3038351969","https://openalex.org/W3040722812","https://openalex.org/W3089233602","https://openalex.org/W3098333777","https://openalex.org/W3151605865","https://openalex.org/W3164684077","https://openalex.org/W3193153957","https://openalex.org/W3195112625","https://openalex.org/W4221088104","https://openalex.org/W4253937035"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1557607869","https://openalex.org/W2165589608","https://openalex.org/W2366350639","https://openalex.org/W2087496541","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2085564391","https://openalex.org/W2108615321","https://openalex.org/W3093557575"],"abstract_inverted_index":{".This":[0],"work":[1,135],"establishes":[2],"\\(H^1\\)":[3,65,74,95,111,137,157],"-norm":[4,96,112,138,158],"stability":[5,139,159],"and":[6,73,103,140,160],"convergence":[7,104,141],"for":[8,37,78,97,115,149],"an":[9],"L2":[10,52,68,143],"method":[11],"on":[12,25,136,145],"general":[13,98,146],"nonuniform":[14,99,147],"meshes":[15,81,100,118,148],"when":[16,119],"applied":[17],"to":[18,61],"the":[19,26,41,51,94,110,125,133,150],"subdiffusion":[20,151],"equation.":[21],"Under":[22],"mild":[23],"constraints":[24],"time":[27,64],"step":[28],"ratio":[29],"\\(\\rho_k\\)":[30],",":[31,40],"such":[32],"as":[33],"\\(0.4573328\\leq":[34],"\\rho_k\\leq":[35],"3.5615528\\)":[36],"\\(k\\geq":[38],"2\\)":[39],"positive":[42,71],"semidefiniteness":[43,72,156],"of":[44,67,105,127,142],"a":[45],"crucial":[46],"bilinear":[47],"form":[48],"associated":[49],"with":[50,82],"fractional-derivative":[53],"operator":[54],"is":[55,101,113,132],"proved.":[56],"This":[57],"result":[58],"enables":[59],"us":[60],"derive":[62],"long":[63],"-stability":[66,75],"schemes.":[69],"These":[70],"properties":[76],"hold":[77],"standard":[79],"graded":[80,117],"grading":[83],"parameter":[84],"\\(1\\lt":[85],"r\\leq":[86],"3.2016538\\)":[87],".":[88,123],"In":[89],"addition,":[90],"error":[91],"analysis":[92],"in":[93,109],"provided,":[102],"order":[106],"\\((5-\\alpha":[107],")/2\\)":[108],"proved":[114],"modified":[116],"\\(r\\gt":[120],"5/\\alpha":[121],"-1\\)":[122],"To":[124],"best":[126],"our":[128],"knowledge,":[129],"this":[130],"study":[131],"first":[134],"methods":[144],"equation.KeywordsL2-type":[152],"methodsubdiffusion":[153],"equationgraded":[154],"meshpositive":[155],"convergenceMSC":[161],"codes35R1165M12":[162]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
