{"id":"https://openalex.org/W4404306607","doi":"https://doi.org/10.1090/mcom/4048","title":"Optimal balanced-norm error estimate of the LDG method for reaction-diffusion problems II: The two-dimensional case with layer-upwind flux","display_name":"Optimal balanced-norm error estimate of the LDG method for reaction-diffusion problems II: The two-dimensional case with layer-upwind flux","publication_year":2024,"publication_date":"2024-11-13","ids":{"openalex":"https://openalex.org/W4404306607","doi":"https://doi.org/10.1090/mcom/4048"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4048","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4048","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","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/A5057836481","display_name":"Yao Cheng","orcid":"https://orcid.org/0000-0001-9500-9398"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yao Cheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108064895","display_name":"Xuesong Wang","orcid":"https://orcid.org/0000-0002-5327-1088"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuesong Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044512711","display_name":"Martin Stynes","orcid":"https://orcid.org/0000-0003-2085-7354"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Stynes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"357","first_page":"73","last_page":"103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991000294685364,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991000294685364,"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":0.991599977016449,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9848999977111816,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6760718822479248},{"id":"https://openalex.org/keywords/flux","display_name":"Flux (metallurgy)","score":0.5186302065849304},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4957827031612396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46653300523757935},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45317935943603516},{"id":"https://openalex.org/keywords/upwind-scheme","display_name":"Upwind scheme","score":0.4504259526729584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36729511618614197},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.34619414806365967},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2699010372161865},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.17719349265098572},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.1540294885635376},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.14514991641044617},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06526276469230652}],"concepts":[{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6760718822479248},{"id":"https://openalex.org/C68709404","wikidata":"https://www.wikidata.org/wiki/Q1134475","display_name":"Flux (metallurgy)","level":2,"score":0.5186302065849304},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4957827031612396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46653300523757935},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45317935943603516},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.4504259526729584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36729511618614197},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.34619414806365967},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2699010372161865},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.17719349265098572},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.1540294885635376},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.14514991641044617},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06526276469230652},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4048","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4048","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W982144962","https://openalex.org/W1476132770","https://openalex.org/W1546297107","https://openalex.org/W1568980822","https://openalex.org/W1987826592","https://openalex.org/W1990397455","https://openalex.org/W1994912903","https://openalex.org/W2005171998","https://openalex.org/W2009874724","https://openalex.org/W2012938047","https://openalex.org/W2045945452","https://openalex.org/W2059030063","https://openalex.org/W2060713120","https://openalex.org/W2061478941","https://openalex.org/W2072532635","https://openalex.org/W2084627977","https://openalex.org/W2099888904","https://openalex.org/W2211063485","https://openalex.org/W2494995535","https://openalex.org/W2506466695","https://openalex.org/W3032521632","https://openalex.org/W3130282808","https://openalex.org/W3172514620","https://openalex.org/W3213887780","https://openalex.org/W4234587664","https://openalex.org/W4254735241","https://openalex.org/W4280561001","https://openalex.org/W4283208200","https://openalex.org/W4297899457","https://openalex.org/W4378213766","https://openalex.org/W4385335115","https://openalex.org/W4387514488","https://openalex.org/W4400246467","https://openalex.org/W4404306607"],"related_works":["https://openalex.org/W2081375188","https://openalex.org/W4390079155","https://openalex.org/W958550505","https://openalex.org/W1604457177","https://openalex.org/W4243253839","https://openalex.org/W81385163","https://openalex.org/W2075483394","https://openalex.org/W9401332","https://openalex.org/W2119683836","https://openalex.org/W1991619102"],"abstract_inverted_index":{"A":[0],"singularly":[1,163],"perturbed":[2,164],"reaction-diffusion":[3,165],"problem":[4,248],"posed":[5],"on":[6,80,254],"the":[7,39,42,56,67,81,87,91,94,98,121,147,172,197,204,228,234,240],"unit":[8],"square":[9],"in":[10,90,138,159,196,209,221,227],"R":[11],"2":[12],"\\mathbb":[13],"{R}^2":[14],"is":[15,144,152,175,203,233,250,260],"solved":[16],"numerically":[17],"by":[18,59,262],"a":[19,61,71,104,139,153,255],"local":[20],"discontinuous":[21],"Galerkin":[22],"(LDG)":[23],"finite":[24],"element":[25],"method.":[26,123,230],"Typical":[27],"solutions":[28,161],"of":[29,32,41,70,120,126,178,206,217,236,247],"this":[30,142,245],"class":[31,246],"2D":[33],"problems":[34],"exhibit":[35],"boundary":[36,57,88],"layers":[37,45,58],"along":[38],"sides":[40],"domain;":[43],"these":[44,114],"generally":[46],"cause":[47],"difficulties":[48],"for":[49,157,162,239,252],"numerical":[50,263],"methods.":[51],"Our":[52,124],"LDG":[53,122,173,229,241],"method":[54,174,242],"handles":[55],"using":[60],"Shishkin":[62,256],"mesh":[63,83,207],"and":[64,151,213,249],"also":[65],"introducing":[66],"new":[68],"concept":[69],"\u201clayer-upwind":[72],"flux\u201d\u2014a":[73],"discrete":[74,127],"flux":[75,128],"whose":[76],"values":[77],"are":[78,111,225],"chosen":[79],"fine":[82],"(which":[84],"lies":[85],"inside":[86],"layers)":[89],"direction":[92,212],"where":[93,200],"layer":[95],"weakens.":[96],"On":[97],"coarse":[99],"mesh,":[100],"one":[101],"can":[102],"use":[103],"standard":[105],"central":[106],"flux.":[107],"No":[108],"penalty":[109],"terms":[110],"needed":[112],"with":[113],"fluxes,":[115],"unlike":[116],"many":[117],"other":[118],"variants":[119],"choice":[125],"makes":[129],"it":[130],"feasible":[131],"to":[132,244],"derive":[133],"an":[134],"optimal-order":[135],"error":[136],"analysis":[137],"balanced":[140,198],"norm;":[141],"norm":[143,150],"stronger":[145],"than":[146],"usual":[148],"energy":[149],"more":[154],"appropriate":[155],"measure":[156],"errors":[158],"computed":[160],"problems.":[166],"It":[167],"will":[168],"be":[169],"proved":[170],"that":[171],"usually":[176],"convergent":[177],"order":[179],"O":[180],"(":[181,182],"N":[183,188,201,202],"\u2212":[184],"1":[185,192],"ln":[186],"\u2061":[187],")":[189,193],"k":[190,219,220],"+":[191],"O((N^{-1}\\ln":[194],"N)^{k+1})":[195],"norm,":[199],"number":[205],"intervals":[208],"each":[210,222],"coordinate":[211,223],"tensor-product":[214],"piecewise":[215],"polynomials":[216],"degree":[218],"variable":[224],"used":[226],"This":[231],"result":[232],"first":[235],"its":[237],"kind":[238],"applied":[243],"optimal":[251],"convergence":[253],"mesh.":[257],"Its":[258],"sharpness":[259],"confirmed":[261],"experiments.":[264]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
